Question

Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 60 miles/hour. The highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles/hour. The records show that exactly 5% of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Answer 1

Solution:-

Given that,

mean = = 60

x = 80

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95  

z = 1.645

Using z-score formula,

x = z * +

80 = 1.645 * + 60

= 80 - 60 / 1.645

= 12.2