Question

Terri Vogel, an amateur motorcycle racer, averages 129.97 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.27 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 128.54 and 131.06 seconds.

c. The fastest 4% of laps are under  seconds.

d. The middle 40% of her laps are from  seconds to  seconds.

Answer 1

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Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(0.4802, TRUE)" & "=NORM.S.DIST(-0.6300, TRUE)" to find the probability.

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.04 to the right of the normal curve or use excel formula "=NORM.S.INV(1-0.04)" to find the z-score.

Round to 4 decimal places.

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Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.70 to the left of the normal curve or use excel formula "=NORM.S.INV(0.70)" to find the z-score.

Round to 4 decimal places.

Round to 4 decimal places.

The middle 40% of her laps are from seconds to   seconds.