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 .

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.

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