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The weight of an organ in adult males has a bell-shaped distribution with a mean of 350 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following.
(a) About 68% of organs will be between what weights?
(b) What percentage of organs weighs between 275 grams and 425 grams?
(c) What percentage of organs weighs less than 275 grams or more than 425 grams?
(d) What percentage of organs weighs between 325 grams and 400 grams?

Sagot :

Using the Empirical Rule, it is found that:

a) About 68% of organs will be between 325 and 375 grams.

b) 99.7% of organs weighs between 275 grams and 425 grams.

c) 0.3% of organs weighs less than 275 grams or more than 425 grams.

d) 81.5% of organs weighs between 325 grams and 400 grams.

What is the Empirical Rule?

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem:

  • The mean is of 350 grams.
  • The standard deviation is of 25 grams.

Item a:

Within 1 standard deviation of the mean, hence:

350 - 25 = 325.

350 + 25 = 375.

About 68% of organs will be between 325 and 375 grams.

Item b:

Within 75 grams of the mean, hence within 3 standard deviations, so 99.7% of organs weighs between 275 grams and 425 grams.

Item c:

More than 3 standard deviations from the mean, hence 100 - 99.7 = 0.3% of organs weighs less than 275 grams or more than 425 grams.

Item d:

Between 1 standard deviation below the mean and 2 above. Considering the symmetry of the normal distribution:

[tex]P = 0.68(50) + 0.95(50) = 81.5[/tex]

81.5% of organs weighs between 325 grams and 400 grams.

To learn more about the Empirical Rule, you can take a look at https://brainly.com/question/24537145

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