Question

Terri Vogel, an amateur motorcycle racer, averages 129.88 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the proportion of her laps that are completed between 130.88 and 132.59 seconds. c. The fastest 3% of laps are under seconds. d. The middle 80% of her laps are from seconds to seconds.

Answer 1

a) The distribution of X is normal

b)

c)

Z-value for fastest 3% interval will be 1.881

Hence, the fastest 3% of laps are under 1.881 * 2.26 + 129.88 = 134.14

d)

Lower limit = 129.88 - 1.284 * 2.26 = 126.98

Upper limit = 129.88 + 1.284 * 2.26 = 132.78

Note - Post any doubts/queries in comments section.