Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 148 minutes with a standard deviation of 14 minutes. Consider 49 of the races.Let X= the average of the 49 races.Part (a)Give the distribution of X. (Round your standard deviation to two decimal places.) Part (b)Find the probability that the average of the sample will be between 147 and 151 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c)Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) minPart (d)Find the median of the average running times.

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Answered: Suppose that a category of world class…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 148 minutes with a standard deviation of 14 minutes. Consider 49 of the races.

Let X= the average of the 49 races.

Part (a)

Give the distribution of
X.
(Round your standard deviation to two decimal places.)
Part (b)

Find the probability that the average of the sample will be between 147 and 151 minutes in these 49 marathons. (Round your answer to four decimal places.)
Part (c)

Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
min
Part (d)

Find the median of the average running times.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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