The mean of the commute time to work for a resident of a certain city is 27.8 mi

Question

The mean of the commute time to work for a resident of a certain city is 27.8 minutes. Assume that the standard deviation of the commute time is 6.6 minutes to complete parts (a) through (c). What are the commute times within 2.5 standard deviations of the mean? (a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the mean? (b) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean? What are the commute times within 1.5 standard deviations of the mean?

Explanation / Answer

Ans:

Chebyshev's inequality is the theorem most often used in stats. It states that no more than 1/k2 of a distribution's values are more than “k” standard deviations away from the mean.

a)1-1/2^2=1-0.25=0.75

75%

b)1-1/1.5^2=1-0.4444=0.5556

55.56%

What are the commute times within 1.5 standard deviations of the mean

lower limit=27.8-1.5*6.6=17.9

upper limit=27.8+1.5*6.6=37.7

c)commute times within 2.5 standard deviations of the mean:

lower limit=27.8-2.5*6.6=11.3

upper limit=27.8+2.5*6.6=44.3

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