Data & Statistics

Problem 1

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

See Solution

Problem 2

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

See Solution

Problem 3

The probability of an athlete not winning 3 races is $\frac{1}{4}$ . Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

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Problem 4

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

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Problem 5

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

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Problem 6

A box has 24 fruits: 7 cherries, 8 oranges, 9 lemons. How many lemons must be sold for cherry pick probability to be 50%? A. 0 B. 1 C. 2 D. 3

See Solution

Problem 7

Calculate the total fuel cost from the transaction: 35.270 L at \$1.619/L, with HST included of \$6.57. Total: \$57.10.

See Solution

Problem 8

Draw a Venn diagram for 400 Grade 7 students: 200 play ML only, 85 play COD only, and 50 play neither.

See Solution

Problem 9

Represent the swim meet results of Danny, John, Kenny, and Sean in a matrix format based on their placements.

See Solution

Problem 10

In a survey of 400 Grade 7 students, find how many play both $\mathrm{ML}$ and $\mathrm{COD}$ using a Venn diagram.

See Solution

Problem 11

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah?
1. Skor Adi = 21
2. Skor Medina = 44
3. Total skor = 52

See Solution

Problem 12

Calculate the cost of capital for Golden Fleece Financial using: debt \$300,000, yield 8\%, shares 10,000, price \$50, book value \$25, return 15\%.

See Solution

Problem 13

Deux amis comparent leurs frais de parking : 2,50€ pour 50 min et 3,50€ pour 1 h 10 min. Le prix est-il proportionnel au temps ?

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Problem 14

Given a table of student activities, find the probability a senior is in sports:
$P(\text{sports} \mid \text{senior}) = \frac{P(\text{sports and senior})}{P(\text{senior})} = [?]\%$
Round to the nearest whole percent.

See Solution

Problem 15

Given a class table, find the probability a student is a sophomore if they are female:
$P(\text{sophomore} \mid \text{female}) = \frac{P(\text{sophomore and female})}{P(\text{female})} = [?] \%$
Round to the nearest whole percent.

See Solution

Problem 16

Find the probability a student is in sports or work using the table. Round $\mathrm{P}(\text{sports or work})$ to the nearest percent.

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Problem 17

Find the probability a sophomore is in drama: $\mathrm{P}(\text{drama} \mid \text{sophomore}) = \frac{\mathrm{P}(\text{drama and sophomore})}{\mathrm{P}(\text{sophomore})} = [?]\%$ . Round to the nearest whole percent.

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Problem 18

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male:
$\mathrm{P}(\text { junior } \mid \text { male })=[?] \%$ Round to the nearest whole percent.

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Problem 19

Which function best fits the data: $y=10 x+2$ , $y=8 x+2$ , $y=5(2)^{x}$ , or $y=2(5)^{x}$ ? Data: $(0,2), (1,10), (2,50), (3,250), (4,1250)$ .

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Problem 20

Calculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

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Problem 21

Is the Garamycin dose of $35 \mathrm{mg}$ every $6 \mathrm{h}$ safe for a $42 \mathrm{lb}$ child? Justify your answer.

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Problem 22

A child weighing 32 lb needs acetaminophen. Calculate mg in 1/2 tsp and check if it's safe based on 25-35 mg/kg/day.

See Solution

Problem 23

Is a $600 \mathrm{mg}$ dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the $150-350 \mathrm{mg}$ daily range?

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Problem 24

Is a dose of Eryped drops $120 \mathrm{mg}$ every 6 hours safe for a 27-pound child given the safe range of $30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

See Solution

Problem 25

A child weighs 29 pounds. Find the safe Digoxin dose range in mg/day for a weight under 15 kg: $11.3-18.8 \mathrm{mg} / \mathrm{kg}$ .

See Solution

Problem 26

A child weighs 29 pounds. Is a dose of $0.125 \mathrm{mg}$ every 12 hours safe, given the range $11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

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Problem 27

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

See Solution

Problem 28

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

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Problem 29

Find the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

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Problem 30

Identify which statements are true or false regarding confidence intervals and distributions.

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Problem 31

Draw a Venn diagram for 400 Grade 7 students: 200 play ML only, 85 play COD only, and 50 play neither.

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Problem 32

Prepare Receipts and Payments Account and Income and Expenditure Account for Readers Club, Ranchi for year ending 31st March 2021.

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Problem 33

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula $E[X]$ y $\operatorname{Var}[X]$ .

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Problem 34

Tenemos dos urnas con bolas de diferentes colores. Encuentra la probabilidad de extraer una bola blanca y, si es blanca, de qué urna proviene.

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Problem 35

Um zootecnista testa nova ração para coelhos. Qual média deve ser superior para trocar a ração atual? (A) 5,0 (B) 9,5 (C) 10,0 (D) 10,5 (E) 15,0.

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Problem 36

Compare the strikeout fractions: Home team: $\frac{12}{32}$ , Visiting team: $\frac{15}{35}$ . Which is greater?

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Problem 37

Roll a fair die twice. Find the probability that the sum is > 5 (Event A) and divisible by 2 or 4 (Event B). Round to two decimals.

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Problem 38

Mr. Heng started a bike business with \$10,000. He bought 20 bikes at \$400 each, sold 12 at \$500 each, and had \$200 in expenses.
a) Create a profit or loss statement. b) Create a financial position statement.

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Problem 39

Find the largest value of $x$ in the student revision hours data if the median is 3. Hours: 1, 2, 3, 4, 5.

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Problem 40

In a class of 30 students, 12 play basketball, 13 play baseball, and 10 play both. Find the probability a student plays either sport.

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Problem 41

In a class of 30 students, 15 play basketball, 16 play baseball, and 7 play both. Find the probability a student plays either sport.

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Problem 42

Find the probability that a randomly chosen student from a class of 20 plays basketball or baseball, given 5 play basketball, 6 play baseball, and 2 play both.

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Problem 43

What is the probability that all three marbles drawn from a bag of 5 red, 8 blue, and 4 green are blue?

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Problem 44

What is the probability that all three drawn marbles are blue from a bag with 8 red, 6 blue, and 3 green marbles?

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Problem 45

What is the probability of a death being from an automobile accident given 56 out of 1,283 deaths? Calculate: $\frac{56}{1283}$ .

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Problem 46

What is the probability that a top executive reads Time or U.S. News given $P(T) = 0.35$ , $P(U) = 0.36$ , and $P(T \cap U) = 0.12$ ?

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Problem 47

What is the probability that the first person selected is in management or supervision from a group of 2270 employees?

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Problem 48

What is the probability of a death being due to an automobile accident from 1,283 total deaths: $56 / 1,283$ ?

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Problem 49

A company has 125 employees with the following absence probabilities: $0$ days (0.60), $1$ day (0.20), $2$ days (0.12), $3$ days (0.04), $4$ days (0.04), $5$ days (0.00). Find the mean days absent.

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Problem 50

Find the producer surplus for selling an item at $\$ 15$ with the demand equation $q=6.1 \cdot(p-2)$ .

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Problem 51

What is the probability of randomly selecting the correct answer: A: $25\%$ , B: $0\%$ , C: $50\%$ , D: $25\%$ ?

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Problem 52

Find scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

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Problem 53

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

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Problem 54

Find the score's location $x$ from the mean using standard deviation for these cases: a. $x=31.2$ , $\mu=23.5$ , $\sigma=8.3$ ; b. $x=151.4$ , $\mu=187.4$ , $\sigma=50.1$ ; c. $x=301.21$ , $\mu=257.89$ , $\sigma=34.71$ .

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Problem 55

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

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Problem 56

Find the mean and standard deviation for these data sets: a. Set $A$ : below 12.3, above 17.8. b. Set $B$ : below 3.51, above 41.16. c. Set $C$ : below 12.41, above 35.12.

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Problem 57

Find the probability that a computer has an internet speed > 8.7 Mbps, given mean = 5.5 Mbps, SD = $1.6 \mathrm{Mbps}$ .

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Problem 58

Check if $X$ is an outlier for these sets: a. $\mu=12.3, \sigma=2.1, X=8.0$ b. $\mu=21.75, \sigma=7.4, X=15.13$ c. $\mu=51.13, \sigma=5.41, X=41.75$ d. $\mu=14.13, \sigma=1.3, X=10.1$

See Solution

Problem 59

Find the percentage of aloe vera plants with heights between $8.0 \mathrm{~cm}$ and $13.2 \mathrm{~cm}$ , given average $10.6 \mathrm{~cm}$ and SD $1.3 \mathrm{~cm}$ .

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Problem 60

Find the percentage of blood samples with coagulation time > 16.5 minutes, given mean = 10 min, SD = 6.5 min.

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Problem 61

A scientist tests guava's effectiveness in filtering waste water. What is the probability that it absorbs more than $80 \mathrm{ppm}$ ?

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Problem 62

Find the probability that more than $0.03 \mathrm{~g}$ of steel is lost, given an average loss of $0.06 \mathrm{~g}$ and a standard deviation of $0.015 \mathrm{~g}$ .

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Problem 63

Describe a distribution that is NOT normally distributed.

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Problem 64

Calculate yearly depreciation for a van purchased for \$55,000 with a residual value of \$5,000 over 4 years using: a. straight-line, b. units-of-production, c. double-declining-balance methods.

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Problem 65

Calculate yearly depreciation for a van costing \$50,000 with a residual value of \$5,000 over 4 years using: a. Straight-line b. Units-of-production c. Double-declining-balance methods.

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Problem 66

Calculate the 5-unit moving average of the function $f(x) = x^3 - x$ .

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Problem 67

Find missing frequencies f1 and f2 for the intervals 0-20, 20-40, 40-60, 60-80, 80-100, 100-120 with mean 57.6 and sum 50.

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Problem 68

Fullen Machinery invests \$400M in equipment with a \$700M future cash flow. How will this affect stock price from \$36? A. \$33.50 B. \$37.50 C. \$39.50

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Problem 69

Calculate Smt. Karak's total income for 2023-24 using the following:
Business income: $20,000 + 46,000 - 12,000 + 18,000$ ; House property: $38,000$ ; Capital gain: $44,000 - 21,000$ ; Other sources: $12,000 + 12,000$ ; Losses: $20,000 + 8,000 + 5,000$ .

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Problem 70

Mr. Madhusudhan sold assets in 2022-23. Calculate his income for 2023-24 given sale proceeds, costs, and inflation indices.

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Problem 71

Find the conversion factor from Wiffles to Inches using the table and fill in the missing values.

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Problem 72

Find the scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

See Solution

Problem 73

Calculate the inflation rate from 2015 to 2016 using CPI: $\text{Inflation Rate} = \frac{CPI_{2016} - CPI_{2015}}{CPI_{2015}} \times 100$

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Problem 74

Calculate the inflation rate from 2015 (CPI = 114.7) to 2016 (CPI = 124.5). Choose the correct option: a. $8.5\%$ , b. $14.7\%$ , c. $9.8\%$ , d. $7.9\%$ .

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Problem 75

Mike wants to evaluate Hi-Tech Inc. stock. Calculate annual returns from 2009 to 2012, find standard deviation, and determine if the coefficient of variation is below 0.90 for investment.

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Problem 76

An urn has $w$ white, $b$ black, and $r$ red balls. Find the probability of drawing a white ball before a black ball for: a) replacement; b) no replacement.

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Problem 77

Jamie Wong wants to build a portfolio with stocks L (40%) and M (60%). Calculate:
a. Expected return $r_{p}$ for each year (2013-2018). b. Average return $\bar{r}_{p}$ over 6 years. c. Standard deviation $\sigma_{r_{p}}$ over 6 years. d. Correlation of returns for stocks L and M. e. Benefits of diversification in the portfolio.

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Problem 78

Jamie Wong's portfolio has stocks L (40%) and M (60%). Calculate: a) annual return $r_{p}$ , b) average return $\bar{r}_{p}$ , c) standard deviation $\sigma_{r_{p}}$ , d) correlation of returns, e) diversification benefits.

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Problem 79

Calculate the rate of return for each investment: A: $-\$800$ , $1,100$ , $100$ ; B: $15,000$ , $120,000$ , $118,000$ ; C: $7,000$ , $45,000$ , $48,000$ ; D: $80$ , $600$ , $500$ ; E: $1,500$ , $12,500$ , $12,400$ .

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Problem 80

Which food (P, Q, R, or S) has the lowest glycaemic index based on amylose and amylopectin percentages: $P(30\%,70\%)$ , $Q(24\%,76\%)$ , $R(14\%,86\%)$ , $S(20\%,80\%)$ ?

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Problem 81

1. Given exam scores: 92, 73, 86, 74, 69, 39, 64, 87, 85, 94, 60, 91, 40, 69, 60, 66, 76, 89, 71, 38, 80, 96, 69. a) Create a relative frequency table (lower limit 38, width 9). b) Draw a relative frequency histogram. c) Find mode. d) Find median. e) Find mean. f) Find standard deviation. g) Find range. h) Find score at the $65^{\text{th}}$ percentile. i) Find percentile of 80. j) Create a stemplot. k) Create a boxplot.

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Problem 82

Find the relative error of a car's speed measured as $48 \mathrm{~km} / \mathrm{h}$ , rounded to the nearest $\mathrm{km} / \mathrm{h}$ .

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Problem 83

A jogging track is $500 \mathrm{~m}$ long with a $0.1 \%$ error. What is the scale interval of the measuring tool?

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Problem 84

Find the max absolute error, measured time, and percentage error for $t$ with $25.465 \leq t < 25.475$ .

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Problem 85

Find the percentage error in measuring an elephant's weight, capped at $5825 \mathrm{~kg}$ , with a $10 \mathrm{~kg}$ scale.

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Problem 86

Bình gieo xúc sắc 100 lần. Tính xác suất số chấm chẵn và số chấm lớn hơn 2 từ kết quả: 1: 15, 2: 20, 3: 18, 4: 22, 5: 10, 6: 15.

See Solution

Problem 87

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

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Problem 88

Find the score's position $x$ relative to the mean using standard deviation for: a. $x=31.2$ , $\mu=23.5$ , $\sigma=8.3$ ; b. $x=151.4$ , $\mu=187.4$ , $\sigma=50.1$ ; c. $x=301.21$ , $\mu=257.89$ , $\sigma=34.71$ .

See Solution

Problem 89

Find the probability that a computer's internet speed exceeds 8.7 Mbps, given an average of 5.5 Mbps and a standard deviation of $1.6 \mathrm{Mbps}$ .

See Solution

Problem 90

Find how many standard deviations each score $x$ is from the mean $\mu$ for the given distributions.

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Problem 91

Find the $Z$ -score for these Math test scores: mean = 36, standard deviation = 8. Scores: 26, 39, 42, 32, 37.

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Problem 92

Find the $Z$ -score for a student who scored 74 on a test with an average of 80 and a standard deviation of 6.

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Problem 93

Determine if a 100-m dash time of 24.7 seconds is satisfactory given $\mu=28.5$ and $\sigma=3.1$ .

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Problem 94

Check if $X$ is an outlier using $\mu$ and $\sigma$ for these scores: a. $X=8.0$ , $\mu=12.3$ , $\sigma=2.1$ ; b. $X=15.13$ , $\mu=21.75$ , $\sigma=7.4$ ; c. $X=41.75$ , $\mu=51.13$ , $\sigma=5.41$ ; d. $X=10.1$ , $\mu=14.13$ , $\sigma=1.3$ .

See Solution

Problem 95

Find Patrick's $Z$ -score if he scored 85 on a test with a mean of 100 and a standard deviation of 15.

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Problem 96

Test if the mean score of sober subjects is 35 using scores: mean = 41, std dev = 3.7, n = 20, significance = 0.01.
Test if the proportion of women (65%) favoring gun control is higher than men (60%) using samples of 360 women and 220 men, significance = 0.05.

See Solution

Problem 97

What is the initial height of a tennis ball dropped from 17.4 cm after $t$ seconds?

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Problem 98

Determine the Moon phase symbol for March 28 from the given options: a. First Quarter, b. Full, c. Last Quarter, d. New, e. None.

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Problem 99

Commuters and parking spaces data: a) Find the correlation coefficient. b) Find critical values for $r$ . c) Check for significant correlation at 0.05 level. d) State the conclusion.
CPI and subway fare data: a) Find regression equation with CPI as $x$ . b) Predict subway fare for CPI = 182.5.

See Solution

Problem 100

Find probabilities for lemonade consumption: more than 21 gallons, less than 19 gallons, and between 20-25 gallons. Also, find sodium probabilities for dinners and construct a confidence interval for garlic's effect on cholesterol.

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Data & Statistics

Problem 1

Find the z z z-score for x=7 x=7 x=7 given a random variable X X X with mean 4 and standard deviation 2.

Problem 2

Find the z z z-score for x=7 x=7 x=7 given that the mean is 4 and the standard deviation is 2.

Problem 3

The probability of an athlete not winning 3 races is 14 \frac{1}{4} 41​. Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

Problem 4

Find the z z z-score for x=7 x = 7 x=7 given that the mean μ=4 \mu = 4 μ=4 and standard deviation σ=2 \sigma = 2 σ=2.

Problem 5

Find the z z z-score for x=7 x = 7 x=7 given μ=4 \mu = 4 μ=4 and σ=2 \sigma = 2 σ=2 using z=x−μσ z = \frac{x - \mu}{\sigma} z=σx−μ​.

Problem 6

A box has 24 fruits: 7 cherries, 8 oranges, 9 lemons. How many lemons must be sold for cherry pick probability to be 50%? A. 0 B. 1 C. 2 D. 3

Problem 7

Calculate the total fuel cost from the transaction: 35.270 L at \$1.619/L, with HST included of \$6.57. Total: \$57.10.

Problem 8

Draw a Venn diagram for 400 Grade 7 students: 200 play ML only, 85 play COD only, and 50 play neither.

Problem 9

Represent the swim meet results of Danny, John, Kenny, and Sean in a matrix format based on their placements.

Problem 10

In a survey of 400 Grade 7 students, find how many play both ML \mathrm{ML} ML and COD \mathrm{COD} COD using a Venn diagram.

Problem 11

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah? 1. Skor Adi = 212. Skor Medina = 443. Total skor = 52

Problem 12

Calculate the cost of capital for Golden Fleece Financial using: debt \$300,000, yield 8\%, shares 10,000, price \$50, book value \$25, return 15\%.

Problem 13

Deux amis comparent leurs frais de parking : 2,50€ pour 50 min et 3,50€ pour 1 h 10 min. Le prix est-il proportionnel au temps ?

Problem 14

Problem 15

Problem 16

Find the probability a student is in sports or work using the table. Round P(sports or work)\mathrm{P}(\text{sports or work})P(sports or work) to the nearest percent.

Problem 17

Problem 18

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male: P( junior ∣ male )=[?]% \mathrm{P}(\text { junior } \mid \text { male })=[?] \% P( junior ∣ male )=[?]% Round to the nearest whole percent.

Problem 19

Which function best fits the data: y=10x+2y=10 x+2y=10x+2, y=8x+2y=8 x+2y=8x+2, y=5(2)xy=5(2)^{x}y=5(2)x, or y=2(5)xy=2(5)^{x}y=2(5)x? Data: (0,2),(1,10),(2,50),(3,250),(4,1250)(0,2), (1,10), (2,50), (3,250), (4,1250)(0,2),(1,10),(2,50),(3,250),(4,1250).

Problem 20

Calculate the expected value of winnings with payouts 2,3,4,5,62, 3, 4, 5, 62,3,4,5,6 and probabilities 0.40,0.20,0.17,0.13,0.100.40, 0.20, 0.17, 0.13, 0.100.40,0.20,0.17,0.13,0.10. Round to the nearest hundredth.

Problem 21

Is the Garamycin dose of 35mg35 \mathrm{mg}35mg every 6h6 \mathrm{h}6h safe for a 42lb42 \mathrm{lb}42lb child? Justify your answer.

Problem 22

A child weighing 32 lb needs acetaminophen. Calculate mg in 1/2 tsp and check if it's safe based on 25-35 mg/kg/day.

Problem 23

Is a 600mg600 \mathrm{mg}600mg dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the 150−350mg150-350 \mathrm{mg}150−350mg daily range?

Problem 24

Is a dose of Eryped drops 120mg120 \mathrm{mg}120mg every 6 hours safe for a 27-pound child given the safe range of 30−50mg/kg/day30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}30−50mg/kg/day?

Problem 25

A child weighs 29 pounds. Find the safe Digoxin dose range in mg/day for a weight under 15 kg: 11.3−18.8mg/kg11.3-18.8 \mathrm{mg} / \mathrm{kg}11.3−18.8mg/kg.

Problem 26

A child weighs 29 pounds. Is a dose of 0.125mg0.125 \mathrm{mg}0.125mg every 12 hours safe, given the range 11.3−18.8mg/kg/day11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}11.3−18.8mg/kg/day?

Problem 27

True or false: For a population proportion confidence interval, we use z\mathrm{z}z-distribution, not t\mathrm{t}t-distribution.

Problem 28

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known σ\sigmaσ and Z, 4) unknown σ\sigmaσ and S, 5) t vs z for population proportion.

Problem 29

Find the test statistic zzz for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at α=0.05\alpha = 0.05α=0.05.

Problem 30

Identify which statements are true or false regarding confidence intervals and distributions.

Problem 31

Draw a Venn diagram for 400 Grade 7 students: 200 play ML only, 85 play COD only, and 50 play neither.

Problem 32

Prepare Receipts and Payments Account and Income and Expenditure Account for Readers Club, Ranchi for year ending 31st March 2021.

Problem 33

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula E[X]E[X]E[X] y Var⁡[X]\operatorname{Var}[X]Var[X].

Problem 34

Tenemos dos urnas con bolas de diferentes colores. Encuentra la probabilidad de extraer una bola blanca y, si es blanca, de qué urna proviene.

Problem 35

Um zootecnista testa nova ração para coelhos. Qual média deve ser superior para trocar a ração atual? (A) 5,0 (B) 9,5 (C) 10,0 (D) 10,5 (E) 15,0.

Problem 36

Compare the strikeout fractions: Home team: 1232\frac{12}{32}3212​, Visiting team: 1535\frac{15}{35}3515​. Which is greater?

Problem 37

Roll a fair die twice. Find the probability that the sum is > 5 (Event A) and divisible by 2 or 4 (Event B). Round to two decimals.

Problem 38

Mr. Heng started a bike business with \$10,000. He bought 20 bikes at \$400 each, sold 12 at \$500 each, and had \$200 in expenses. a) Create a profit or loss statement. b) Create a financial position statement.

Problem 39

Find the largest value of xxx in the student revision hours data if the median is 3. Hours: 1, 2, 3, 4, 5.

Problem 40

In a class of 30 students, 12 play basketball, 13 play baseball, and 10 play both. Find the probability a student plays either sport.

Problem 41

In a class of 30 students, 15 play basketball, 16 play baseball, and 7 play both. Find the probability a student plays either sport.

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

The probability of an athlete not winning 3 races is $\frac{1}{4}$ . Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

In a survey of 400 Grade 7 students, find how many play both $\mathrm{ML}$ and $\mathrm{COD}$ using a Venn diagram.

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah?
1. Skor Adi = 21
2. Skor Medina = 44
3. Total skor = 52

Find the probability a student is in sports or work using the table. Round $\mathrm{P}(\text{sports or work})$ to the nearest percent.

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male:
$\mathrm{P}(\text { junior } \mid \text { male })=[?] \%$ Round to the nearest whole percent.

Which function best fits the data: $y=10 x+2$ , $y=8 x+2$ , $y=5(2)^{x}$ , or $y=2(5)^{x}$ ? Data: $(0,2), (1,10), (2,50), (3,250), (4,1250)$ .

Calculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

Is the Garamycin dose of $35 \mathrm{mg}$ every $6 \mathrm{h}$ safe for a $42 \mathrm{lb}$ child? Justify your answer.

Is a $600 \mathrm{mg}$ dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the $150-350 \mathrm{mg}$ daily range?

Is a dose of Eryped drops $120 \mathrm{mg}$ every 6 hours safe for a 27-pound child given the safe range of $30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

A child weighs 29 pounds. Find the safe Digoxin dose range in mg/day for a weight under 15 kg: $11.3-18.8 \mathrm{mg} / \mathrm{kg}$ .

A child weighs 29 pounds. Is a dose of $0.125 \mathrm{mg}$ every 12 hours safe, given the range $11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}$ ?

True or false: For a population proportion confidence interval, we use $\mathrm{z}$ -distribution, not $\mathrm{t}$ -distribution.

Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known $\sigma$ and Z, 4) unknown $\sigma$ and S, 5) t vs z for population proportion.

Find the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

Marcos tiene 5 monedas. a) ¿Cuál es la probabilidad de obtener 3 cruces al lanzarlas? b) Calcula $E[X]$ y $\operatorname{Var}[X]$ .

Compare the strikeout fractions: Home team: $\frac{12}{32}$ , Visiting team: $\frac{15}{35}$ . Which is greater?

Mr. Heng started a bike business with \$10,000. He bought 20 bikes at \$400 each, sold 12 at \$500 each, and had \$200 in expenses.
a) Create a profit or loss statement. b) Create a financial position statement.

Find the largest value of $x$ in the student revision hours data if the median is 3. Hours: 1, 2, 3, 4, 5.

What is the probability of a death being from an automobile accident given 56 out of 1,283 deaths? Calculate: $\frac{56}{1283}$ .

What is the probability that a top executive reads Time or U.S. News given $P(T) = 0.35$ , $P(U) = 0.36$ , and $P(T \cap U) = 0.12$ ?

What is the probability of a death being due to an automobile accident from 1,283 total deaths: $56 / 1,283$ ?

A company has 125 employees with the following absence probabilities: $0$ days (0.60), $1$ day (0.20), $2$ days (0.12), $3$ days (0.04), $4$ days (0.04), $5$ days (0.00). Find the mean days absent.

Find the producer surplus for selling an item at $\$ 15$ with the demand equation $q=6.1 \cdot(p-2)$ .

What is the probability of randomly selecting the correct answer: A: $25\%$ , B: $0\%$ , C: $50\%$ , D: $25\%$ ?

Find scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

Find the probability density function of a normal distribution with mean 1 and standard deviation $\frac{1}{2}$ .

Is a 24.7-second 100-m dash satisfactory if last year's average was $\mu=28.5$ and $\sigma=3.1$ ? Explain.

Find the mean and standard deviation for these data sets: a. Set $A$ : below 12.3, above 17.8. b. Set $B$ : below 3.51, above 41.16. c. Set $C$ : below 12.41, above 35.12.

Find the probability that a computer has an internet speed > 8.7 Mbps, given mean = 5.5 Mbps, SD = $1.6 \mathrm{Mbps}$ .

Find the percentage of aloe vera plants with heights between $8.0 \mathrm{~cm}$ and $13.2 \mathrm{~cm}$ , given average $10.6 \mathrm{~cm}$ and SD $1.3 \mathrm{~cm}$ .

A scientist tests guava's effectiveness in filtering waste water. What is the probability that it absorbs more than $80 \mathrm{ppm}$ ?

Find the probability that more than $0.03 \mathrm{~g}$ of steel is lost, given an average loss of $0.06 \mathrm{~g}$ and a standard deviation of $0.015 \mathrm{~g}$ .

Calculate the 5-unit moving average of the function $f(x) = x^3 - x$ .

Find the scores at 1, 2, and 3 standard deviations above the mean for: a. $\mu=13.2$ , $\sigma=4.2$ ; b. $\mu=86.1$ , $\sigma=12.5$ ; c. $\mu=521.4$ , $\sigma=81.7$ .

Calculate the inflation rate from 2015 to 2016 using CPI: $\text{Inflation Rate} = \frac{CPI_{2016} - CPI_{2015}}{CPI_{2015}} \times 100$

Calculate the inflation rate from 2015 (CPI = 114.7) to 2016 (CPI = 124.5). Choose the correct option: a. $8.5\%$ , b. $14.7\%$ , c. $9.8\%$ , d. $7.9\%$ .