Professor Gersch grades his exams and sees that the grades are normally distributed with a mean of 77 and a standard deviation of 6.Based on the Empirical Rule, between what two grades should you expect to find roughly the middle 95% of the distribution?a. 65 to 89b. 77 to 83c. 71 to 83d. 77 to 89e. 59 to 95

The correct option is a. 65 to 89.

Step-by-step explanation:

According to the Empirical Rule in a normal distribution with mean µ and standard-deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

•68% data falls within 1 standard deviation of the mean. That is P (µ-σ≤X≤ µ+σ) = 0.68.

•95% data falls within 2 standard deviations of the mean. That is P (µ-2σ≤X≤ µ+2σ) = 0.95.

•99.7% data falls within 3 standard deviations of the mean. That is P (µ-3σ≤X≤ µ+3σ) = 0.997.

The information provided is:

Use the Empirical rule to compute the middle 95% of the distribution as follows:

Thus, the correct option is a. 65 to 89.

step-by-step explanation:

first, eliminate the parenthesis:

3

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2

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second, group like terms:

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4

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third, combine like terms:

(

3

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4

)

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→

−

1

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→

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2