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When gordon lived in the chicago area, it took him 35 min. to commute to his workplace. he recently took a new job and moved to the stevens point area in wisconsin, and his commuting time to work became only 18 min. however, compared to chicago, the distribution of commuting time to work in the stevens point area has a lower mean (15.6 min), with a standard deviation of 5.6 min. in which of those areas (chicago vs. stevens point) was gordon’s commuting time longer, relative to other workers in the same area?

User Fehbari
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Final answer:

Gordon's commuting time was likely longer relative to other workers in Chicago compared to in Stevens Point because his commute time in Chicago was well above the mean for large US cities, whereas in Stevens Point, it was only slightly above the mean.

Step-by-step explanation:

When trying to determine whether Gordon's commuting time was longer relative to other workers in the same area, we need to look at how his commute compares to the average commute time, taking into account the standard deviation for the area.

In the Chicago area, we do not have the mean or standard deviation provided, but in the Stevens Point area, the mean is 15.6 minutes with a standard deviation of 5.6 minutes. Gordon's new commute time of 18 minutes is only slightly above the mean for Stevens Point. To compare his commute time in each area, we use the concept of standard score or z-score, which measures how many standard deviations an element is from the mean. A z-score is calculated by subtracting the mean from the individual data point and dividing by the standard deviation.

Without specific data for Chicago, it is hard to calculate the exact z-score, but considering the mean commute time for the 15 largest US cities is 25.4 minutes and Gordon's commute was 35 minutes, his Chicago commute time was likely much higher above the mean than his Stevens Point time, assuming Chicago's standard deviation isn't significantly larger. Therefore, it's reasonable to infer that Gordon's commute time was longer relative to other workers in Chicago compared to Stevens Point.

User Alexrgs
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