Problem

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1529 and the standard deviation was 311 . The test scores of four students selected at random are $1960,1260,2220$, and 1430. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
The z-score for 1960 is
(Round to two decimal places as needed.)
The z-score for 1260 is
(Round to two decimal places as needed.)
The $z$-score for 2220 is
(Round to two decimal places as needed.)
The $z$-score for 1430 is
(Round to two decimal places as needed.)
Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The unusual value(s) is/are
(Use a comma to separate answers as needed.)
B. None of the values are unusual.

Answer

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Answer

\(\boxed{2220}\) is the unusual value.

Steps

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. In this case, the mean is 1529 and the standard deviation is 311. We can calculate the z-scores for each of the four students' test scores using this formula.

Step 2 :A z-score of less than -2 or greater than 2 is generally considered unusual. After calculating the z-scores, we can check if any of them fall outside this range.

Step 3 :Calculate the z-scores for the test scores 1960, 1260, 2220, and 1430. The z-scores are approximately 1.39, -0.86, 2.22, and -0.32 respectively.

Step 4 :Check if any of the z-scores fall outside the range of -2 to 2. The test score 2220 is considered unusual as its z-score is greater than 2.

Step 5 :\(\boxed{2220}\) is the unusual value.

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