Question

A radar unit is used to measure the speed of cars on a highway during rush hour traffic. The speeds of individual cars are normally distributed with a mean of 55 mph and a standard deviation of 3.2 mph. Find the probability of the following events:
(a) A car traveling faster than average.
(b) A car traveling over 65 mph
(c) A car traveling between 48 and 50 mph.

Answer 1

Mean = = 55

Standard deviation = = 3.2

a)

We have to find the probability that a car traveling faster than average.

That is we have to find P(X > 55)

For finding this probability we have to find z score.

That is we have to find P(Z > 0)

P(Z > 0) = 1 - P(Z < 0) = 1 - 0.5 = 0.5

b)

We have to find the probability that a car traveling over 65 mph.

That is we have to find P(X > 65)

For finding this probability we have to find z score.

That is we have to find P(Z > 3.13)

P(Z > 3.13) = 1 - P(Z < 3.13) = 1 - 0.9991 = 0.0009

c)

We have to find probability that a car traveling between 48 and 50 mph.

That is we have to find P(48 < X < 50)

For finding this probability we have to find z scores.

That is we have to find P( - 2.19 < Z < - 1.56)

P( - 2.19 < Z < - 1.56) = P(Z < - 1.56) - P(Z < - 2.19) = 0.0591 - 0.0144 = 0.0447