Solved on Nov 02, 2023
Probability that a randomly selected teacher in Connecticut makes less than $
STEP 1
Assumptions1. The average teacher's salary in Connecticut is \$57,337. The distribution of salaries is normal3. The standard deviation of the salaries is \$7,5004. We want to find the probability that a randomly selected teacher makes less than \$54,500 per year
STEP 2
To find the probability that a randomly selected teacher makes less than \x\mu\sigma$ is the standard deviation (in this case, \$7,500)
STEP 3
Plug in the values for , , and into the z-score formula.
STEP 4
Calculate the z-score.
STEP 5
Now that we have the z-score, we can find the probability that a randomly selected teacher makes less than \$54,500 per year. This is the same as finding the area to the left of the z-score on the standard normal distribution. We can use a z-table or a calculator to find this probability.
STEP 6
Look up the probability associated with the z-score in a z-table or use a calculator to find the probability.
So, the probability that a randomly selected teacher makes less than \$54,500 per year is0.3520 or35.20%.
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