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 at a gate, is 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 a mean of 2.3 seconds and a standard deviation of 0.02 seconds.

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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Let Y is a random variable show the hill times f... View the full answer