Normal Distribution

Question

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

The fastest 4% of her laps are under how many seconds? (Round your answer to two decimal places.)

Answer 1

4% means an area of 92% from -z to +z, 4% in each tail

with a z score of slightly less than 2, as 2 standard deviations under the empirical rule means 95% with 2.5% in each tail

use z tables or a z calculator, z = -1.751

(x-129.71)/2.28 = -1.751

x = -(1.751)(2.28) + 129.71

x = 125.72 seconds

or less for the top 4% of all lap times