Question

The weight of an organ in adult males has a​ bell-shaped distribution with a mean of 320 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following.​(a) About 99.7​% of organs will be between what​ weights?​(b) What percentage of organs weighs between 275 grams and 365 ​grams?​(c) What percentage of organs weighs less than 275 grams or more than 365 ​grams?​(d) What percentage of organs weighs between 230 grams and 365 ​grams?

Answer 1

Answer:

a) 99.7%

b) 68%

c) 68% of organs weighs between 275 and 365 grams, so 32% of organs weighs will be less than 275 or more than 365 grams.

d) 81.5% of organs weighs between 290 grams and 365 grams.

Step-by-step explanation:

A) 99.7% of organs will be between 3 standard deviation from the mean.

$320 - 3 \times 45 = 185$

$320 + 3 \times 45 = 455$

So 99.7% of organs will be between 185 and 455.

B) 275 grams and 365 grams are 1 standard deviation from the mean.

From empirical rule about 68% data falls within 1 standard deviation from the mean.

So 68% of organs weighs btwn 275 grams and 365 grams.

C) Since 68% of organs weighs between 275 and 365 grams, so 32% of organs weighs will be less than 275 or more than 365 grams.

D) 230 is 2 standard deviation below the mean and 365 is one standard deviation above the mean.

According to the empirical rule, 95% of the observation lies within 2 standard deviations of the mean. Therefore 5% lies outside 2 standard deviations of the mean.

So 95%/2 = 47.5% of organs weighs between the mean and 230 grams.

According to the empirical rule about 68% data falls within one standard deviation from the mean.

so, 68%/2 = 34% of organs weighs between the mean and 365 grams.

So total = 47.5% + 34% = 81.5% of organs weighs between 290 grams and 365 grams.