Question

Dave drives to work each morning at about the same time. his commute time is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. the percentage of time that his commute time exceeds 61 minutes is equal to the area under the standard normal curve that lies to the ___ of ___.

Answer 1

The normal distribution curve is shown in the diagram below

The percentage of time that his commute time exceeds 61 minutes is equal to the area under the standard normal curve that lies to the RIGHT of X=61

Standardising X=61 to find z-score
$z= \frac{61-45}{5} =3.2$

from the z-table
$P(Z\ \textgreater \ 3.2) = 1 - P(Z\ \textless \ 3.2) = 1 - 0.9993 = 0.0007 = 0.07%$