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# Chebyshev's inequality and sample standard deviations

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36) Chebyshev's Inequality According to the US Census Bureau the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following:
(a) What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean?
(b) What minimum percentage of commuters in Boston has a commute time within 1.5 standard deviations of the mean?
40) Identical values Compute the sample standard of deviation of the following test scores: 78, 78, 78, 78. What can be said about a data set in which all the values are identical?
34) Mr. Zuro finds the mean height of all 14 students in his statistics class to be 68.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 65 inches tall. What is the mean height of the 15 students in the class
16) Flight Time The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas Nevada, to Newark, New Jersey, on Continental Airlines.
282, 270, 260, 266, 257, 260, 267
Compute the mean, median, and mode flight time.
1) How would you explain the concept of probability to a child

On first page answer question #26 a, b, and c
On second page answer question #36 a, b, c, d, and e On third page answer question #38 a, b, and c On fourth page answer question #44 On fifth page answer question #56
On sixth page answer question #6 On seventh page answer question #8 a, and b On page eight answer question #24 a, and b On page nine answer question #28
On page ten answer question #20
On page eleven answer question #26 a, and b On page twelve answer question #4
On page thirteen answer question #12

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#### Solution Summary

The solution gives detailed steps on solving various questions on descriptive statistics. All formula and calculations are shown and explained. All necessary graphs are included.

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## Estimate Sample Size N with Chebyshev's Theorem

Suppose that a measurement has mean M and variance = 25.

Let X bar be the average of n such independent measurements. Use Chebychev's inequality to estimate how large n should be such that
P(|X bar - M | < 1) = 0.95.

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