Question

The mean of the commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the commute time is 7.6 minutes to complete parts (a) through (c).

(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 2.5 standard deviations of the mean? What are the commute times within 2.5 standard deviations of the mean?

The minimum percentage of commuters in the city that has a commute time within 2.5 standard deviations of the mean is _____.

The commute times within 2.5 standard deviations of the mean are between ___ and ____ .

(c) What is the minimum percentage of commuters who have commute times between 4.5 minutes and 50.1 minutes?

Answer #1

a)

minimum percentage of commuters in the city has a commute time
within 2 standard deviations of the mean =(1-1/k^{2})*100
=(1-1/2^{2})*100 =75 %

b)

minimum percentage of commuters in the city has a commute time
within 2.5 standard deviations of the mean
=(1-1/2.5^{2})*100 =84.0%

corresponding interval = |
(27.3-2*7.6,27.3+2*7.6)=between 12.1 and 42.5 |

c)

minimum percentage of commuters who have commute times between
4.5 minutes and 50.1 minutes =(1-1/3^{2})*100 =88.9 %

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