Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1507 and the standard deviation was 315. The test scores of four students selected at random are 1900​, 1260​, 2220​, and 1390. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1900 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1260 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 2220 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1390 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.

Answer 1

Solution :

Given that ,

mean = = 1507

standard deviation =  = 315

a) x = 1900

Using z-score formula,

z = x - /   

z = 1900 - 1507 / 315

z = 1.25

b) x = 1260

Using z-score formula,

z = x - /   

z = 1260 - 1507 / 315

z = -0.78

c) x = 2220

Using z-score formula,

z = x - /   

z = 2220 - 1507 / 315

z = 2.26

d) x = 1390

Using z-score formula,

z = x - /   

z = 1390 - 1507 / 315

z = -0.37

The usual values have z-score between  -2.00 and 2.00

correct option is =A

A. The unusual​ value(s) is 2220