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.