A standardized exam\'s scores are normally distributed. In a recent year, the me

Question

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1496 1496 and the standard deviation was 313 313. The test scores of four students selected at random are 1920 1920, 1220 1220, 2190 2190, and 1380 1380. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1920 1920 is nothing . (Round to two decimal places as needed.) The z-score for 1220 1220 is nothing . (Round to two decimal places as needed.) The z-score for 2190 2190 is nothing . (Round to two decimal places as needed.) The z-score for 1380 1380 is nothing . (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 nothing . (Use a comma to separate answers as needed.) B. None of the values are unusual.

Explanation / Answer

Ans:

Given that

mean=1496

standard deviation=313

z=(x-1496)/313

1)when x=1920

z=(1920-1496)/313=1.35

2)when x=1220

z=(1220-1496)/313=-0.88

3)when x=2190

z=(2190-1496)/313=2.22

4)when x=1380

z=(1380-1496)/313=-0.37

As,z score for x=2190 is z=2.22,which is greater than 2,so 2190 is unusual value.

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