The speed is normally distributed with mean μ=64 and standard deviation σ =7. Use the transformation [tex] \frac{X-\mu}{\sigma} [/tex] for calculating the probability. This value is called Z-score.
The Z score is [tex] Z=\frac{71-64}{7} =1 [/tex].
Refer to the standard normal distribution table.
The probability
[tex] P(X>71)=P(Z>1)=1-P(Z<1)=0.1587
[/tex]
Thus, the proportion of the vehicles that are travelling faster than 71 mph is [tex]p=0.1587 [/tex] .
