Question

Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 43 minutes and a standard deviation of 8 minutes. The percentage of time that his commute time lies between 51 and 59 minutes is equal to the area under the standard normal curve between ___ and ___.

Answer 1

Let X denotes the  commute time for Dave to drive to work on a randomly selected morning.

X ~ Normal(43, 8²)

The probability that his commute time lies between 51 and 59 minutes on a randomly selected morning

The percentage of time that his commute time lies between 51 and 59 minutes is = 100*0.135905 = 13.59%

Moreover,

z-score corresponding to 51

z-score corresponding to 59

Hence,

ans-> The percentage of time that his commute time lies between 51 and 59 minutes is equal to the area under the standard normal curve between 1 and 2