Question

The speed of motor vehicles on a certain stretch of road are normally distributed with a mean of 64.2 mph and a standard deviation of 8.44 mph.

What is the probability that a motor vehicle selected at random is traveling at :

a) more than 65 mph?

b) less than 60 mph?

c) between 65 and 80 mph?

Answer 1

a ) P(x> 65) = 0.4641

b) P(x< 60) =0.6915

c) P(65< x<80) = 0.4334

Explanation:

Given data:

`\mu = 64.2`

`\sigma = 8.44`

`z =(x-\mu)/(\sigma)`

a)
`P(x> 65) = P(z> (65 - 64.2)/(8.44))`

= P(z>0.09)

=0.4641

b)
`P(x< 60) = P(z< (60 - 64.2)/(8.44))`

= P(z < 0.50)

=0.6915

c) P(65 < x <80)

`=    P(x<80) - P(x<65)`

`= P(z< (80 - 64.2)/(8.44)) - P(z< (65 - 64.2)/(8.44))`

`= P(z < 1.87) - P(z < 0.09)`

= 0.9693 - 0.5359

= 0.4334