MX racing is a sprint sport where races range from around 30 to 45 seconds depending on the length of the track. Given races are over in such a short time, the start - commonly referred to as gate starts due to everyone lining up on a gate, are critical to success in the sport. A coach with a particular interest in data analysis coaching an elite athlete records data at a local race track for the time it takes their athlete to reach the bottom of the starting hill. The coach has found that the hill times for their athlete follow a normal distribution with mean 2.3 seconds and standard deviation 0.02 seconds. (a) What hill time distinguishes the slowest 10% of hill times?
MX racing is a sprint sport where races range from around 30 to 45 seconds depending on the length of the track. Given races are over in such a short time, the start - commonly referred to as gate starts due to everyone lining up on a gate, are critical to success in the sport. A coach with a particular interest in data analysis coaching an elite athlete records data at a local race track for the time it takes their athlete to reach the bottom of the starting hill. The coach has found that the hill times for their athlete follow a normal distribution with mean 2.3 seconds and standard deviation 0.02 seconds. (a) What hill time distinguishes the slowest 10% of hill times?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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BMX racing is a sprint sport where races range from around 30 to 45 seconds depending on the
length of the track. Given races are over in such a short time, the start - commonly referred to as
gate starts due to everyone lining up on a gate, are critical to success in the sport. A coach with a
particular interest in data analysis coaching an elite athlete records data at a local race track for the
time it takes their athlete to reach the bottom of the starting hill.
The coach has found that the hill times for their athlete follow a
seconds and standard deviation 0.02 seconds.
- (a) What hill time distinguishes the slowest 10% of hill times?
- (b) What is the probability that a randomly selected hill time is less than 2.27 seconds?
- (c) Let X be the number of hill times that are less than 2.27 seconds from 10 separate starts. Assuming the athlete is well rested between starts, what distribution might you consider X to follow. Justify your response by indicating any assumptions you have made.
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