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?
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?
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.
(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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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