Complete question :
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:
a. More than 20 minutes? b. For 20 minutes or less
Answer: 0.0764 ; 0.9236
Explanation:
Mean (m) = 15 minutes
Standard deviation (sd) = 3.5
Z - score :
Z = (x - m) / sd
A) more than 20 minutes
P(X > 20) ; x = 20
Z > (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z > 1.429) = 0.5 - P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 - 0.4236 = 0.0764
2) 20 minutes or less :
P(X <= 20) ; x = 20
Z < (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z < 1.429) = 0.5 + P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 + 0.4236 = 0.9236