1. The branch manager of a credit union examines the accepted and rejected mortgage applications from individuals and businesses in the previous month. The results of the mortgage applications from the previous quarter is shown in the table below.
Individuals Businesses Total
Accepted 141 106 247
Rejected 34 16 50
Total 175 122 297
What is the joint relative frequency for businesses that have accepted mortgage applications? Round to the nearest thousandth.
A. 0.411
B. 0.054
C. 0.475
D. 0.357
2. A group of forest rangers took a sample of the bears on the grounds within a certain national forest to help determine trends in the population. The rangers examined the type of bear (black, brown, and grizzly) as well as whether the bear was male or female.
Male Female Total
Brown Bears 36 39 75
Black Bears 45 42 87
Grizzly Bears 17 19 36
Total 98 100 198
What is the conditional relative frequency that the bear in the sample is female given that the bear is a black bear? Round to three decimal places.
A. 0.420
B. 0.483
C. 0.212
D. 0.517
3. Aidan surveyed teenagers aged 13 to 19 who reside in his town and own either a desktop or laptop computer. The survey asked each teenager whether they use the operating system Doors or Cortland as well as their preference of web browsers Gozilla and Adventure. The results of Aidan's survey are shown in the accompanying table.
Doors Cortland Totals
Gozilla 54 14 68
Adventure 11 67 78
Total 65 81 146
Which category has the greatest marginal relative frequency?
A. Teenagers in Aidan's town who use the Gozilla web browser.
B. Teenagers in Aidan's town who use the Adventure web browser.
C. Teenagers in Aidan's town who use the Adventure web browser and the Cortland operating system.
D. Teenagers in Aidan's town who use the Cortland operation system.
4. How does finding the conditional relative frequency for a cell in a two-way frequency table differ from finding the joint relative frequency?
A. Conditional relative frequency is found by multiplying a joint relative frequency by a marginal relative frequency while the joint relative frequency is found by dividing a joint frequency by a marginal frequency.
B. Conditional relative frequency is found by dividing a marginal frequency by the total frequency while the joint relative frequency is found by dividing the joint frequency by the total frequency.
C. Conditional relative frequency is found by dividing a joint frequency by a marginal frequency while the joint relative frequency is found by dividing a joint frequency of the cell by the total frequency.
D. Conditional relative frequency is found by dividing a joint frequency by the total frequency while the joint relative frequency is found by dividing a marginal frequency by the total frequency.
5. A certain professional football league changed the line of scrimmage for a point-after touchdown kick attempt from the 2-yard line to the 15-yard line starting in the 2015 season. The table below shows the number of made and missed point-after touchdown kick attempts for the 2014 and 2015 seasons.
2014 2015 Total
Made 1,222 1,146 2,368
Missed 8 71 79
Total 1,230 1,217 2,447
How does the likelihood for a miss in the 2015 season compare to the likelihood for a miss in the 2014 season?
A. The marginal relative frequency for an attempt during the 2015 season is 0.497, which is slightly less than the marginal relative frequency for an attempt during the 2014 season, 0.503.
B. The conditional relative frequency for a missed attempt given that it occurred in the 2015 season is 0.942, which is less than the conditional relative frequency for a missed attempt during the 2014 season, 0.993.
C. The conditional relative frequency for a missed attempt given that it occurred in the 2015 season is 0.058, which is much greater than the conditional relative frequency for a missed attempt during the 2014 season, 0.007.
D. The joint relative frequency for a missed attempt during the 2015 season is 0.029, which is greater than the joint relative frequency for a missed attempt during the 2014 season, 0.003.
1. C. 0.475
2. D. 0.517
3. A. Teenagers in Aidan's town who use the Gozilla web browser.
4. C. Conditional relative frequency is found by dividing a joint frequency by a marginal frequency while the joint relative frequency is found by dividing a joint frequency of the cell by the total frequency.
5. A. The marginal relative frequency for an attempt during the 2015 season is 0.497, which is slightly less than the marginal relative frequency for an attempt during the 2014 season, 0.503.