College students average 7.6 hours

Question

College students average 7.6 hours of sleep per night with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of college students sleep for more than 8.9 hours?

Probability =

Answer 1

Mean = 7.6 hours, std deviation = 0.67 hours

x = hours sleep

want to find P(x > 8.9)

convert x = 8.9 from N(7.6, 0.67) to standard normal N(0,1) via transformation:

Z = (x - mean)/std = (8.9 - 7.6)/0.67 = 1.94

P(x > 8.9) --> P(z > 1.94) = P(z < -1.94) = 0.0262