Question

A traffic study of 2,500 vehicles that passed by a checkpoint showed that their speeds were normally distributed with a mean of 82.5 kph and a standard deviation of 11.5 kph. How many vehicles had a speed of more than 90 kph? *

Answer 1

Solution:

$\bar x = 82.5$

$s = 11.5$

$P(X>90)=1-P(X\le90)=1-P(Z\le\frac{90-\bar x}{s})=$

$=1-P(Z<\frac{90-82.5}{11.5})=1-P(Z<0.65)=1-0.74215=0.25785=25.785\%$

25.785% of 2500 vehicles = $2500 \times 0.25785=644.625\approx645$

Thus, 645 vehicles have a speed of more than 90kph.