Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile l

Question

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-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. In words, define the random variable X the distance (in miles) of each lap in time (in seconds) per race the time (in seconds) per lap the distance (in miles) of each race Give the distribution of X X - (-) Find the percent of her laps that are completed in less than 132 seconds. % The fastest 4% of her laps are under how many seconds? sec Enter your answers to two decimal places. The middle 70% of her lap times are from seconds to seconds

Explanation / Answer

a) time (in seconds) per lap

b) X~N(129.71,2.282)

c)P(X<132)=P(Z<(132-129.71)/2.28)=P(Z<1.0044)=0.8424~84.24%

d)fastest 4% ; zscore =-1.7507

hence corresponding time =129.71-1.7507*2.28=125.72

e) for middle 70% CI, z=1.0364

hence interval =mean -/+ z*std deviation =127.35 to 132.07

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