Chapter 12, Problem 24PT4

To determine

To find: If a particular Western gorilla is known to weigh 345 pounds approximately how much would a cappuccino monkey have to weigh to have the same standardized weight as of lowland gorilla.

Options

(a) 4.08

(b) 7.27

(c) 7.93

(d) 8.20

(e) Not enough information given.

Western lowland gorillas have mean weight of 275 pounds and the standard deviation 40 pounds. Cappuccino monkeys have a mean weight of 6 pounds and the standard deviation of 1.1 pounds. Both gorillas and and monkeys’ weight is normally distributed.

Answer to Problem 24PT4

If a particular Western gorilla is known to weigh 345 pounds approximately how much would a cappuccino monkey have to weigh to have the same standardized weight as of lowland gorilla is 7.93 pounds. Correct choice is (c).

Explanation of Solution

The standardized weight of gorilla is obtained by subtracting actual weight by mean weight and dividing result by standard deviation. Symbolically, where z is standardized weight and x is actual weight. Hence standardized weight of gorilla is

For monkey to have a standard weight of 1.75,

Actual weight should be

z*1.1+6=1.75*1.1+6=7.925 Because X=z&*#963;+µ . Hence actual weight of monkey should be 7.925 pounds. When rounded it is 7.93 pounds.

Correct choice is (c).