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

$\mu=82.5 \\ \sigma= 11.5 \\ P(X>90) = 1 -P(X<90) \\ = 1 -P(Z< \frac{90-82.5}{11.5}) \\ = 1 -P(Z< 0.652) \\ = 1 -0.7428 \\ = 0.2572 \\ N = 2500 \times 0.2572 = 643$

Answer: 643