Question

A traffic study of 1,600 vehicles that passed by a checkpoint showed that their speeds were normally distributed with a mean of 97.6 kph and a standard deviation of 10.4 kph. How many vehicles had a speed of more than 100 kph?

Answer 1

$\bar x = 97.6$

$s = 10.4$

$P(X>100)=1-P(X<100)=1-P(Z<\frac{100-\bar x}{s})=$

$=1-P(Z<\frac{100-97.6}{10.4})=1-P(Z<0.23)=1-0.591=0.409$

40.9% of 1600 vehicles:

$1600 * 0.409= 654$

Answer: 654 vehicles have a speed of more than 100kph.