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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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