the weight of an organ in adult males has a bellshaped distr

the weight of an organ in adult males has a bell-shaped distribution with a mean of 330grams and a standard deviation of 30 grams. Use the empirical rule to determine the following.

(A)about 95% of organs will be between what weight?

(B) what percentage of organs weights between 240 grams and 420 grams?

(C) what percentage of organs weights less than 240 grams and more than 420 grams?

(D) what percentage of organs weights between 240 grams and 390 grams?

Solution

a)

95% are within 2 standard deviations. Thus,

lower bound = u - 2*sigma = 330 - 2*30 = 270
upper bound = u + 2*sigma = 330 + 2*30 = 390

Thus, between 270 and 390. [ANSWER]

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b)

Here,

z = (x - u)/sigma

Thus, for x = 420,

z = (420-330)/30 = 3

For x = 240,

z = (240-330)/30 = -3

Thus, within 3 standard deviations is 99.7% of the data. [ANSWER]

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c)

Thus, outside the interval in B) is 100%-99.7% = 0.3% [answer]

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d)

For 390,

z = (390-330)/30 = 2

For 240, z = -3 as earlier.

By empirical rule, between the mean and z = 2 is approximately 47.5% of the data.

Also by empirical rule, between the mean and z = -3 is 49.85% of the data.

Thus, that is a total of 49.85% + 47.7% = 97.35% [ANSWER]