Answer to Question #263982 in Statistics and Probability for GYI

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

$\bar x = 82.5$

$\sigma = 11.5$

$P(X>90)=1-P(X<90) \\ =1-P(Z<\frac{90-82.5}{11.5})$

$=1-P(Z<\frac{90-82.5}{11.5}) \\ =1-P(Z<0.652) \\ =1-0.7427\\ =0.2573$

25.73% of 2500 vehicles:

$2500 \times 0.2573= 643$

Answer: 643 vehicles have a speed of more than 90 kph.