Question

1. the table below gives the conditional relative frequency by column. suppose that 97 cats were examined, and 15 were purebred. determine the raw data for the remaining categories.

conditional relative frequency by column

	mixed breed	purebred	total
bred	0.049	0.533	0.124
total	1.000	1.000	1.000

raw data

	mixed breed	purebred	total
bred
total		15	97

Explanation:

Step1: Find number of mixed - breed cats

The total number of cats is 97 and the number of pure - bred cats is 15. So the number of mixed - breed cats is $97 - 15=82$.

Step2: Calculate number of adopted pure - bred cats

The conditional relative frequency of adopted pure - bred cats is 0.467 and the total number of pure - bred cats is 15. So the number of adopted pure - bred cats is $0.467\times15\approx7$.

Step3: Calculate number of bred pure - bred cats

The conditional relative frequency of bred pure - bred cats is 0.533 and the total number of pure - bred cats is 15. So the number of bred pure - bred cats is $0.533\times15\approx8$.

Step4: Calculate number of adopted mixed - breed cats

The conditional relative frequency of adopted mixed - breed cats is 0.951 and the number of mixed - breed cats is 82. So the number of adopted mixed - breed cats is $0.951\times82\approx78$.

Step5: Calculate number of bred mixed - breed cats

The conditional relative frequency of bred mixed - breed cats is 0.049 and the number of mixed - breed cats is 82. So the number of bred mixed - breed cats is $0.049\times82\approx4$.

Step6: Calculate number of adopted cats

The number of adopted cats is the sum of adopted pure - bred and adopted mixed - breed cats, $7 + 78=85$.

Step7: Calculate number of bred cats

The number of bred cats is the sum of bred pure - bred and bred mixed - breed cats, $8+4 = 12$.

Answer:

	Mixed Breed	Purebred	Total
Bred	4	8	12
Total	82	15	97