Question

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour.

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Calculate the Z value for the next car that passes through the checkpoint will be traveling more than 66 miles per hour.

Calculate the probability that the next car will be traveling more that 66 miles per hour is:

Answer 1

Solution :

Given that ,

mean = = 61

standard deviation =  = 4

a) x = 65

Using z-score formula,

z = x - /   

z = 65 - 61 / 4

z = 1.00

b) x = 66

Using z-score formula,

z = x - /   

z = 66 - 61 / 4

z = 1.25

c) P(x > 66) = 1 - p( x< 66)

=1- p P[(x - ) / < (66 - 61) / 4 ]

=1- P(z < 1.25)

Using z table,

= 1 - 0.8944

= 0.1056