Question

A city council collected data on driving speeds in order to decide on appropriate speed limits. On a major street the mean speed was 38.6 mph, with a standard deviation of 4.3 mph. On a residential street, speeds had a mean of 22.1 mph and a standard deviation of 2.4 mph. Relative to the other traffic on that street, which of the following speeds is greater: 49 mph on the major street or 28 mph on the residential street? Show the calculations that justify your answer, round the results to two decimal places

Answer 1

The speed comparison between two different values of two different streets can be done by calculating the Z score, whichever Z score is more with respect to their street will have the more relative speed. Now Z score calculated as

$Z= \frac{X-\bar{X}}{\sigma}$

$\bar{X}= Mean$$\sigma=Standard, deviation$

Now for major street

$Z=\frac{49-38.6}{4.3}=2.419$

And for Residential Stree

$Z=\frac{28-22.1}{2.4}=2.458$

Hence by calculating Z score it is clearly evident that relative to the other traffic speed 28 mph on street road has more speed.