The weight of an organ in adult males has a bell-shaped distribution with a mean of 340 grams and a standard deviation of 30 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 280 grams and 400 grams? (c) what percentage of organs weighs less than 280 grams or more than 400 grams? (d) what percentage of organs weighs between 250 grams and 400 grams?

a) 99.7% of the organs will be between 250 and 420 grams.

b) 95% of the organs weighs between 280 grams and 400 grams.

c) 5% of the organs weighs less than 280 grams or more than 400 grams.

d) 97.5% of the organs weighs between 250 grams and 400 grams.

Step-by-step explanation:

The mean value of the weight of an organ is 340 grams and the standard deviation is 30 grams, so .

(a) About 99.7% of organs will be between what weights?

The Empirical Rule states that 99.7% of the values of X of a set with mean and standard deviation belong to the following interval

We have that , so:

99.7% of the organs will be between 250 and 420 grams.

(b) What percentage of organs weighs between 280 grams and 400 grams?

280 grams is 2 standard deviations below the mean.

400 grams is 2 standard deviations above the mean.

The Empirical rule states that 95% of the weights of the organs are between 2 standard deviations of the mean, so

95% of the organs weighs between 280 grams and 400 grams.

(c) What percentage of organs weighs less than 280 grams or more than 400 grams?

95% of the organs weighs between 280 grams and 400 grams. This means that 5% of the organs weighs less than 280 grams or more than 400 grams.

(d) What percentage of organs weighs between 250 grams and 400 grams?

250 grams is 3 standard deviations below the mean.

The Empirical rule states that 50% of the weights are above the mean, and 50% are below. Of those that are below, 100% weights at least 3 standard deviations below the mean.

400 grams is 2 standard deviations above the mean.

Of the values that are above the mean, 95% of them are at most 2 standard deviations above the mean.

So:

97.5% of the organs weighs between 250 grams and 400 grams.

answer: slight chance that it will happen

step-by-step explanation: