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 .

B = { square numbers less than 30 }.

or

B = {x/x is square of a whole number; }

Step-by-step explanation:

Given the set B

B={ 0,1,4,9,16,25}

Let us check the elements in set B.

It is clear that each element in set B is a square of a whole number.

Thus, we can specify set of B by giving a written description of Its element in a variety of ways, such as:

B = { square numbers less than 30 }.

or

B = {x/x is square of a whole number; }