The speeds of cars on the highway have a mean of 95 kmh with

The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h.

a) What percentage of cars averaged less than 85 km/h?

b) If a police car stopped cars that were going more than 105 km/h, how many cars would they stop if there were 8000 cars on the highway?

Solution

Speed of the car follows N(95,5)

a) P(X <85) = P(Z < (85 - 95)/5) = P( Z < -2) = 0.0228

Therefore 2.28% of cars averaged less than 85 km/h

b) P (X > 105) = P(Z > (105 - 95)/5) = P( Z > 2) = 1- P(Z<2) = 1- 0.9772 = 0.0228

As there are 8000 cars on the highway so = 8000 * 0.0228 = 182. 4 = 182 cars police will stop on highway with speed more than 105 km/h