Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 142 minutes with a standard deviation of 15 minutes. Consider 49 of the races. Let X = the average of the 49 races. O Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) O Part (b) Find the probability that the average of the sample will be between 140 and 145 minutes in these 49 marathons. (Round your answer to four decimal places.) O Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Please label each part.

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 142 minutes with a standard deviation of 15 minutes. Consider 49 of the races.
Let X
= the average of the 49 races.
O Part (a)
Give the distribution of X. (Round your standard deviation to two decimal places.)
O Part (b)
Find the probability that the average of the sample will be between 140 and 145 minutes in these 49 marathons. (Round your answer to four decimal places.)
O Part (c)
Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
min
O Part (d)
Find the median of the average running times.
min
Transcribed Image Text:Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 142 minutes with a standard deviation of 15 minutes. Consider 49 of the races. Let X = the average of the 49 races. O Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) O Part (b) Find the probability that the average of the sample will be between 140 and 145 minutes in these 49 marathons. (Round your answer to four decimal places.) O Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min O Part (d) Find the median of the average running times. min
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