Problem

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 20.7 and the standard deviation was 5.4 . The test scores of four students selected at random are 14, 22, 8, and 36 . Find the z-scores that correspond to each value and determine whether anv of the values are unusual.

The z-score for 14 is .
(Round to two decimal places as needed.)
The z-score for 22 is .
(Round to two decimal places as needed.)
The z-score for 8 is .
(Round to two decimal places as needed.)
The z-score for 36 is .

Answer

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Answer

In a normal distribution, any z-score greater than 3 or less than -3 is considered unusual. Therefore, none of the scores are unusual, which is the final answer None of the scores are unusual.

Steps

Step 1 :Calculate the z-score for each student using the formula z=Xμσ, where X is the student's score, μ is the mean, and σ is the standard deviation.

Step 2 :For the student with a score of 14, the z-score is calculated as z=1420.75.4=1.24 (rounded to two decimal places).

Step 3 :For the student with a score of 22, the z-score is calculated as z=2220.75.4=0.24 (rounded to two decimal places).

Step 4 :For the student with a score of 8, the z-score is calculated as z=820.75.4=2.35 (rounded to two decimal places).

Step 5 :For the student with a score of 36, the z-score is calculated as z=3620.75.4=2.83 (rounded to two decimal places).

Step 6 :In a normal distribution, any z-score greater than 3 or less than -3 is considered unusual. Therefore, none of the scores are unusual, which is the final answer None of the scores are unusual.

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