Among U.S. cities with a population of more than 250,000, the mean one-way commu

Question

Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 37.9 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 6.9 minutes.

What percent of the New York City commutes are for less than 29 minutes?

What percent are between 29 and 35 minutes?

What percent are between 29 and 42 minutes?

What percent of the New York City commutes are for less than 29 minutes?

What percent are between 29 and 35 minutes?

What percent are between 29 and 42 minutes?

Explanation / Answer

Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.2 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.0 minutes.

(a) What percent of the New York City commutes are for less than 28 minutes?

(b) What percent are between 28 and 33 minutes?

(c) What percent are between 28 and 46 minutes?

All of these are done by using Z-scores and checking it against a z-score/percentile table (http://www.measuringusability.com/pcalcz... (be sure to click one sided) or using a TI-83/4 type '2nd' 'VARS' 'normalcdf(' and enter a lower bound and an upper bound of your z score (for more information on thishttp://tibasicdev.wikidot.com/normalcdf ) ).

You calculate z score with this formula:
z = ( x - xbar ) / s
x=observation
xbar=mean
s=standard deviation

(a) z = ( 28 - 38.2 ) / 7 = -1.4571 (put this number into z-score/percentile calc)
7.2544%

(b) for this one just take the percent that are under 33 min - percent under 28 min
z = (33 - 38.2 ) / 7 = -.7428
22.8801 - 7.2544 = 15.6257%

(c) same method as for (b)
z = (46 - 38.2 ) / 7 = 1.1142
86.7403 - 7.2544 = 78.4859%

Source:

http://www.measuringusability.com/pcalcz...
http://tibasicdev.wikidot.com/normalcdf

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