Problem

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1483 and the standard deviation was 318 . The test scores of four students selected at random are 1900,1200, 2170, and 1380 Find the z-scores that correspond to each value and determine whether any of the values are unusual. The $z$-score for 1900 is 1.31 (Round to two decimal places as needed.) The $z$-score for 1200 is -0.89 (Round to two decimal places as needed.) The $z$-score for 2170 is (Round to two decimal places as neect.)

Solution

Step 1 :The z-score is a measure of how many standard deviations an element is from the mean. To find the z-score of a value, we subtract the mean from the value and then divide by the standard deviation.

Step 2 :In this case, we need to find the z-score for the value 2170. The mean is 1483 and the standard deviation is 318.

Step 3 :Subtract the mean from the value: 2170 - 1483 = 687

Step 4 :Divide the result by the standard deviation: 687 / 318 = 2.160377358490566

Step 5 :Round the result to two decimal places: 2.16

Step 6 :Final Answer: The z-score for 2170 is \(\boxed{2.16}\).

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Source: https://solvelyapp.com/problems/7476/

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