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Free_Kalibri [48]
3 years ago
13

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

on 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?
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0

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

= 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

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