Question

The average speed of a car driving down freeway is 70mph with a standard deviation of 5mph. Thid speed is normally distributed. Find the following.A) what is the probability that a randomly selected car is driving more than 77mph?B) what is probability that a randomly selected car is driving between 65 and 69 mph?C) what is the probability that a randonly selected car is driving between 67 and 77mph?D) what is the probability that a randomly selected car is driving less than 77mph?

Answer 1

0.081,0.2621,0.645,0.919

Explanation:

Let X be the average speed of a car driving down freeway

Given that X is normal with mean as 70mph with a standard deviation of 5mph.

To convert to Z score we do

`Z =(x-70)/(5)`

a) the probability that a randomly selected car is driving more than 77mph

`=P(X>77)\\=P(Z>1.4)\\=0.081`

b) probability that a randomly selected car is driving between 65 and 69 mph

=
`P(-1<z<-0.2)\\=0.2621`

c) the probability that a randonly selected car is driving between 67 and 77mph

=
`P(-0.6<z<1.4)\\\\=0.645`

d) the probability that a randomly selected car is driving less than 77mph

`=P(Z<1.4) = 0.919`