Answer:
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.