Problema Solution

In a set of 95 ACT​ scores, where the mean is 21 and the standard deviation is 5.39

(a) how many scores are expected to be lower than 15.61 ​(one standard deviation below the​ mean)?

(b) How many of the 95 scores are expected to be below 31.78​(two standard deviations above the​ mean)?

Answer provided by our tutors

(a)

z=(15.61-21)/5.39

z = -1

P(z<-1)=0.1587

Number of scores expected to be lower than 15.61 is 0.1587*95 = 15 scores.

(b)

z=(31.78-21)/5.39

z = 2

P(z<2)=0.9772

Number of scores expected to be lower than 31.78 is 0.9772*95 = 93 scores.