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