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.

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

hope it will

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