Question

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 21.3 and the standard deviation was 56. The test scores of four students selected at random are 14, 23, 8, and 35. Find the z-scores that correspond to each value and determine whether any of the values are unusual 

Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice 

Answer 1

Mean = 21.3

SD = 5.6

Z = (X – mean)/SD

Z-score for 14:

Z = (14 - 21.3)/5.6

Z = -1.30

The z-score for 14 is -1.30.

P(Z<-1.30) = 0.09619 > 0.05

(by using z-table or excel)

This is not unusual observation.

Z-score for 23:

Z = (23 - 21.3)/5.6

Z =0.303571

The z-score for 23 is 0.30.

P(Z>0.30) = 0.380727 > 0.05

(by using z-table or excel)

This is not unusual observation.

Z-score for 8:

Z = (8 - 21.3)/5.6

Z = -2.375

The z-score for 8 is -2.38.

P(Z<-2.38) = 0.008774 < 0.05

(by using z-table or excel)

This is an unusual observation.

Z-score for 35:

Z = (35 - 21.3)/5.6

Z = 2.446429

The z-score for 35 is 2.45.

P(Z>2.45) = 0.007214 < 0.05

(by using z-table or excel)

This is an unusual observation.

The unusual values are 8, 35.