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?

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08-10-2019
Mathematics

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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?

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rejkjavik rejkjavik · Answer 1 · 2019-10-08T15:56:18+02:00

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.

[tex]320 - 3 \times 45 = 185[/tex]

[tex]320 + 3 \times 45 = 455[/tex]

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.