Question

The weight of an organ in adult males has a bell-shaped distribution with a mean of 300 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following.

(a) About 68% of organs will be between what weights?

(b) What percentage of organs weighs between 165 grams and 435 grams?

(c) What percentage of organs weighs less than 165 grams or more than 435 grams?

(d) What percentage of organs weighs between 255 grams and 435 grams?

(A) _ and _grams. (use ascending order.)

(B) _ % (type an integer or a decimal.)

(C) _ % (type an integer or a decimal.)

(D) _% (type an integer or decimal rounded to two decimal places as needed.)

Answer 1

Solution:- Given that mean = 300, standard deviation = 45

(a) emprical forumla 68% : μ +/- σ

300 -1 (45) = 255
300 + 1 (45) = 345

68% of organs will be between (255, 345)

(b) z1 = (165-300)/45 = -3

z2 = (435-300)/45 = 3

  99.7% of observations lie with in 3 standard deviations of the mean

(c) organs weighs less than 165 grams or more than 435 grams

100 -68 = 32 %

165 = 300 - 2 (50)
435 = 300 + 1 (50)

1-0.997 = 0.003 = 0.3

d)