Question

Speeding: On a stretch of Interstate-89, car speed is a normally distributed variable with a mean of 68.3 mph and a standard deviation of 3.9 mph. Suppose you are a police officer on this stretch of road and only have time to ticket 1% of the cars that go by you. How fast should someone be traveling before you pull them over? Round your answer to 1 decimal place.

Answer 1

Given,

= 68.3 , = 3.9

We convert this to standard normal as

P(X < x) = P(Z < x - / )

We have to calculate x such that,

P(X > x) = 0.01

P(X < x) = 0.99

P(Z < x - / ) = 0.99

From Z table, z-score for the probability of 0.99 is 2.3263

So,

x - / = 2.3263

x - 68.3 / 3.9 = 2.3263

Solve for x

x = 77.4