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

Answer:

a ) P(x> 65) =  0.4641

b) P(x< 60) =0.6915

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

Step-by-step explanation:

Given data:

$\mu = 64.2$

$\sigma = 8.44$

$z =\frac{x-\mu}{\sigma}$

a) $P(x> 65) = P(z> \frac{65 - 64.2}{8.44})$

                  = P(z>0.09)

                  =0.4641

b) $P(x< 60) = P(z< \frac{60 - 64.2}{8.44})$

                  = P(z < 0.50)

                  =0.6915

c) P(65 < x <80)

$=    P(x<80) - P(x<65)$

$= P(z< \frac{80 - 64.2}{8.44}) - P(z< \frac{65 - 64.2}{8.44})$

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

= 0.9693 - 0.5359

= 0.4334