Question

The accompanying cumulative relative frequency distribution summarizes data obtained in a study of the ending overages​ (in dollars) for the cash register balance at a business

Class Frequency Relative Frequency Cumulative Relative Frequency
-60 to -40 3 0.060 0.06
-40 to -20 3 0.060 0.12
-20 to 0 5 0.100 0.22
0 to 20 17 0.340 0.56
20 to 40 19 0.380 0.94
40 to 60 3 0.060 1.00

a. Determine the proportion of the days in which there were no shortages.

Answer 1

The proportion of days with no shortages, when the ending overage was between -20 and 0 dollars, is found by subtracting the cumulative relative frequency of the '-20 to 0' range from the '0 to 20' range, resulting in 34% of the days.

Step-by-step explanation:

The proportion of days in which there were no shortages (ending overages ranging from -20 to 0 dollars) can be determined using the cumulative relative frequency distribution. According to the data, the relative frequency for the '-20 to 0' class is 0.100, and the cumulative relative frequency for this class is 0.22.

To find the proportion of no shortage days, we can simply refer to the cumulative relative frequency value for the '0 to 20' range, which marks the endpoint of no shortages. In this case, the cumulative relative frequency is 0.56. Therefore, the proportion of days with no shortages is the difference between the cumulative relative frequencies of '0 to 20' and '-20 to 0', which is 0.56 - 0.22 = 0.34, or 34% of the days.