Question

Suppose speeds of vehicles on a particular stretch of roadway are normally distributed with a mean of 36, 6mph and a standard deviation of 1.7 mph, what is the probability that out of 3 vehicles a randomly selected vehicle uses a speed of between 35mph and 40mph,

Answer 1

Answer:  

= 36. 6, = 1.7, n=1

We want to find P( 35< x < 40 )

P( 35 < x < 40 ) = P(x < 40) - P(x < 35)

first find P(x < 40)

formula for z-score is

z =2

P(x < 40) = P(Z < 2)

find P(Z < 2) using normal z table we get

P(Z < 2) = 0.9772

P(x < 40) = 0.9772

now find P(x < 35)

formula for z-score is

z = −0.9412

P(x < 35) = P(Z < −0.9412)

find P(Z < −0.9412) using normal z table we get

P(Z < −0.9412) = 0.1733

P(x < 35) = 0.1733

P( 35 < x < 40 ) = P(x < 40) - P(x < 35)

P( 35 < x < 40 ) = 0.9772−0.1733

P( 35 < x < 40 ) = 0.8039

Probability =0.8039