Question

The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?

Answer 1

Answer:

weight of female bears  324

Explanation:

let , the weight of male bears be X

Mean M = 500 and

standard deviation $\sigma _M = 50$

Z score for x = 530 is ,

$z = \frac{x - \mu_M}{\sigma_M} = \frac{530-500}{0.5} =0.6$

Let , weight of female bears be Y

 mean F = 300 and

standard deviation  = 40

Z SCORE  for y  = 530 { given}

Z sore for x = 530 is 0.6

$0.6 = \frac{y - 300}{40}$

solving for y we get

y = 324