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 1200 is -0.89 .
(Round to two decimal places as needed.)
The $z$-score for 2170 is 2.16
(Round to two decimal places as needed.)
The $z$-score for 1380 is -0.32 .
(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. Norie of the values are unusual.

Answer

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Answer

Final Answer: Therefore, the unusual value is \(\boxed{2170}\).

Steps

Step 1 :The z-score is a measure of how many standard deviations an element is from the mean. In this case, we are given the mean and standard deviation of the test scores, and we are asked to find the z-scores for the given test scores. The formula to calculate the z-score is: \(z = \frac{X - \mu}{\sigma}\) where: \(X\) is the element (test score), \(\mu\) is the mean, \(\sigma\) is the standard deviation.

Step 2 :We can use this formula to calculate the z-scores for the given test scores. After that, we can determine if any of the test scores are unusual. A z-score is considered unusual if it is greater than 2 or less than -2, as it means the test score is more than 2 standard deviations away from the mean.

Step 3 :Given that the mean is 1483 and the standard deviation is 318, we can calculate the z-scores for the test scores 1900, 1200, 2170, and 1380. The z-scores are approximately 1.31, -0.89, 2.16, and -0.32 respectively.

Step 4 :Looking at these z-scores, we can see that the test score 2170 is considered unusual because its z-score is greater than 2.

Step 5 :Final Answer: Therefore, the unusual value is \(\boxed{2170}\).

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