According to the U.S. Census Bureau, the mean of the commute time to work for a

Question

According to the U.S. 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 8.1minutes to answer the following:

a) What minimum percentage of commuters in Bostson 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?

C) what is the minimum percentage of commuters who hace commute times between 3 minutes and 51.6 minutes?

Explanation / Answer

a) Minimum percentage of commuters in Boston that has a commute time within 2 standard deviations of the mean

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544

b) Minimum percentage of commuters in Boston that has a commute time within 1.5 standard deviations of the mean

= P(Z < 1.5) - P(Z < -1.5)

= 0.9332 - 0.0668

= 0.8664

c) P(3 < X < 51.6)

= P(X < 51.6) - P(X < 3)

= P(Z < (51.6-27.3)/8.1) - P(Z < (3-27.3)/8.1)

= P(Z < 3) - P(Z < -3)

= 0.9987 - 0.0013

= 0.9974

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