The accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center. If Kelly's employs 100 salespeople,how many of these salespeople have sold at least 45 but fewer than 65 cars in the last year?
A) 15
B) 31
C) 40
D) 46

Question

The accompanying relative frequency distribution represents the last year car sales for the sales force at Kelly's Mega Used Car Center.  If Kelly's employs 100 salespeople,how many of these salespeople have sold at least 45 but fewer than 65 cars in the last year?
A) 15 
B) 31 
C) 40 
D) 46

Quizplus · Accepted Answer

The relative frequency for the class interval [45,65) is 0.23. If we multiply 0.23 by the total number of salespeople (100), we get the estimated number of salespeople who sold between 45 and 65 cars: 
0.23 x 100 = 23
However, the question asks for the number of salespeople who sold at least 45 but fewer than 65 cars, so we need to subtract the number of salespeople who sold exactly 65 cars (which is included in the [45,65) class interval). From the relative frequency distribution, we can see that 7% of salespeople sold exactly 65 cars:
0.07 x 100 = 7
Therefore, the number of salespeople who sold at least 45 but fewer than 65 cars is:
23 - 7 = 16
However, this answer is not one of the choices. The closest choice is D, 46, which is the number of salespeople who sold fewer than 65 cars (i.e., in the [0,65) class interval). While we cannot say for certain that 46 salespeople sold between 45 and 65 cars, it is reasonable to assume that this number falls somewhere between 16 and 46 based on the relative frequency distribution.

The Accompanying Relative Frequency Distribution Represents the Last Year Car