Question

Suppose speeds of vehicles on a particular stretch of roadway are normally distributed with mean 36.6 mph and standard deviation 1.7 mph.

A. Find the probability that the speed X of a randomly selected vehicle is between 35 and 40 mph.

B. Find the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph.

****YOU MUST SHOW ALL OF YOUR WORK TO DOCUMENT HOW YOU ARRIVED AT THE SOLUTION****

Answer 1

Solution :

Given that ,

mean = = 36.6

standard deviation = = 1.7

Using z table,  

P(35< x <40 ) = P[(35-36.6) /1.7 < (x -) / < (40-36.6) / 1.7)]

= P( -0.94< Z <2 )

= P(Z < 2) - P(Z < -0.94)

Using z table,  

= 0.9772-0.1736

=0.8036

b.

n=20

= 36.6

=  / n = 1.7 / 20=0.38

= P(35<    < 40) = P[(35-36.6) /0.38 < ( - ) / < (40-36.6) / 0.38)]

= P(-4.21 < Z <8.95 )

= P(Z < 8.95) - P(Z <-4.21 )

Using z table,  

= 1-0

=1

=