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 normal distribution with mean 2.3 seconds and standard deviation 0.02 seconds.
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) The coach is unable to make it to training one night and asks for the athlete to
complete 10 gate starts. The coach asks the athlete to review the times and let him know how
many out of 10 were faster than 2.27 seconds. The athlete advises the coach that on 4 of the 10
starts they were faster than 2.27 seconds. Calculate the probability of the athlete beating a hill
time of 2.27 seconds on 4 or more of the 10 gate starts.
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So the Probability of the athlete beating a hill
time of 2.27 seconds on 4 or more of the 10 gate starts, will be 99.99%?
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