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/k²)*100 =(1-1/2²)*100 =75 %

b)

minimum percentage of commuters in the city has a commute time within 2.5 standard deviations of the​ mean =(1-1/2.5²)*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 =(1-1/3²)*100 =88.9 %