Solved on Nov 12, 2023

Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

STEP 1

Assumptions1. The mean of the dataset is79.22. The standard deviation of the dataset is7.973. We are looking for the Z-score that represents the70th percentile4. The Z-score is calculated using the formula $Z = \frac{X - \mu}{\sigma}$

STEP 2

First, we need to find the Z-score that corresponds to the70th percentile. In a standard normal distribution, the70th percentile corresponds to a Z-score of approximately0.52. This value can be found in a standard Z-score table or calculated using statistical software.

STEP 3

Now that we have the Z-score, we can plug this into the Z-score formula and solve for $X$ , the score in the70th percentile.
$0.52 = \frac{X -79.22}{7.97}$

STEP 4

First, multiply both sides of the equation by the standard deviation,7.97.
$0.52 \times7.97 = X -79.22$

STEP 5

Calculate the left side of the equation.
$4.14 = X -79.22$

STEP 6

Next, add the mean,79.22, to both sides of the equation to solve for $X$ .
$4.14 +79.22 = X$

STEP 7

Calculate the right side of the equation.
$83.36 = X$ The score that represents the70th percentile in the dataset is approximately83.36.

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Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

STEP 1

Assumptions1. The mean of the dataset is79.22. The standard deviation of the dataset is7.973. We are looking for the Z-score that represents the70th percentile4. The Z-score is calculated using the formula $Z = \frac{X - \mu}{\sigma}$

STEP 2

First, we need to find the Z-score that corresponds to the70th percentile. In a standard normal distribution, the70th percentile corresponds to a Z-score of approximately0.52. This value can be found in a standard Z-score table or calculated using statistical software.

STEP 3

Now that we have the Z-score, we can plug this into the Z-score formula and solve for $X$ , the score in the70th percentile.
$0.52 = \frac{X -79.22}{7.97}$

STEP 4

First, multiply both sides of the equation by the standard deviation,7.97.
$0.52 \times7.97 = X -79.22$

STEP 5

Calculate the left side of the equation.
$4.14 = X -79.22$

STEP 6

Next, add the mean,79.22, to both sides of the equation to solve for $X$ .
$4.14 +79.22 = X$

STEP 7

Calculate the right side of the equation.
$83.36 = X$ The score that represents the70th percentile in the dataset is approximately83.36.

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Find the score in the 70th percentile of a dataset with mean μ=79.22\mu=79.22μ=79.22 and standard deviation σ=7.97\sigma=7.97σ=7.97 using the Z-score formula Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ​.

STEP 1

Assumptions1. The mean of the dataset is79.22. The standard deviation of the dataset is7.973. We are looking for the Z-score that represents the70th percentile4. The Z-score is calculated using the formula Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ​

STEP 2

First, we need to find the Z-score that corresponds to the70th percentile. In a standard normal distribution, the70th percentile corresponds to a Z-score of approximately0.52. This value can be found in a standard Z-score table or calculated using statistical software.

STEP 3

Now that we have the Z-score, we can plug this into the Z-score formula and solve for XXX, the score in the70th percentile.0.52=X−79.227.970.52 = \frac{X -79.22}{7.97}0.52=7.97X−79.22​

STEP 4

First, multiply both sides of the equation by the standard deviation,7.97.0.52×7.97=X−79.220.52 \times7.97 = X -79.220.52×7.97=X−79.22

STEP 5

Calculate the left side of the equation.4.14=X−79.224.14 = X -79.224.14=X−79.22

STEP 6

Next, add the mean,79.22, to both sides of the equation to solve for XXX.4.14+79.22=X4.14 +79.22 = X4.14+79.22=X

STEP 7

Calculate the right side of the equation.83.36=X83.36 = X83.36=XThe score that represents the70th percentile in the dataset is approximately83.36.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

Assumptions1. The mean of the dataset is79.22. The standard deviation of the dataset is7.973. We are looking for the Z-score that represents the70th percentile4. The Z-score is calculated using the formula $Z = \frac{X - \mu}{\sigma}$

Now that we have the Z-score, we can plug this into the Z-score formula and solve for $X$ , the score in the70th percentile.
$0.52 = \frac{X -79.22}{7.97}$

First, multiply both sides of the equation by the standard deviation,7.97.
$0.52 \times7.97 = X -79.22$

Calculate the left side of the equation.
$4.14 = X -79.22$

Next, add the mean,79.22, to both sides of the equation to solve for $X$ .
$4.14 +79.22 = X$

Calculate the right side of the equation.
$83.36 = X$ The score that represents the70th percentile in the dataset is approximately83.36.