Question

The weight of adult male grizzly bears living in the wild continental United States is normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds.

(a) What is the probability that a randomly selected male grizzly bear weighs between 445 and 520 pounds? Make sure to find all appropriate z-scores and show your work.

(b) Approximately what would the weight of a female grizzly bear be with the same standardized score (zscore) as a male grizzly bear with a weight of 460 pounds?

(c) Is a female grizzly bear weighing 400 pounds unusual? Justify your answer.

Answer 1

a)

Let X:Weight of male grizzly bear.

To find

b)  

Let Y be the weight of female bear

c)

Let W be weight of female bear

Hence the probability is very small therefore it is unusual to find a female bear with 400 or greater than 400 pounds of weight.

Thank you !!