# A posted speed limit of 55 miles per hour means

Posted By Admin @ September 03, 2022

#### Question:

Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.

Speed (miles per hour) 45-49 50-54 55-59 60-64 65-69 70-74 75-79
Frequency 10 40 150 175 75 15 10
Total 475a.What is the mean speed of the automobiles traveling on this road? b.Compute the variance and the standard deviation.

(a) Mean = 60.684

(b) Variance = 31.2292                       Standard deviation = 5.5883

Step-by-step explanation:

We are given the following frequency distribution of speeds;

Speed (miles per hour)            Frequency (f)          X                 X * f

45-49                                     10                      47                470

50-54                                    40                      52               2080

55-59                                   150                     57                8550

60-64                                   175                     62                10850

65-69                                   75                      67                5025

70-74                                    15                      72                 1080

75-79                                    10                     77                  770

= 475                           = 28825

(a) Mean speed of the automobiles, = = = 60.684

(b) Variance formula is given by =

This mean variance is given by subtracting each X value from the mean and then squaring each value and then multiplying it with the corresponding frequency.

Variance =

= 31.2292

Standard Deviation = = = 5.5883 .

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