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Part 1

A college's data about the incoming freshmen indicates that the mean of their high school GPAs was

3.23.2,

with a standard deviation of

0.350.35;

the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of

2525.

What might the mean GPA of one of these seminar groups be? Describe the appropriate sampling distribution model, including shape, center, and spread, with attention to assumptions and conditions. Make a sketch using the 68-95-99.7 Rule.

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Part 1

Describe the appropriate sampling distribution model, including shape, center, and spread.

A.

Upper N left parenthesis nothing comma nothing right parenthesisNenter your response here,enter your response here

(Type integers or decimals.)

B.

The sampling distribution model is not Normal because the sample size is less than 30.

Part 2

What assumptions and conditions must be satisfied for the sampling distribution model to be appropriate? Select all that apply.

A.

The students represent less than 10% of all possible students.

B.

Individuals' GPAs are independent.

C.

The distribution of the students' GPAs is Normal.

D.

The distribution of GPAs is roughly unimodal and symmetric, so the sample is large enough.

Part 3

Make a sketch using the 68-95-99.7 Rule. Choose the correct graph below.

A.

2.993.063.133.23.273.343.41MeanGPA99.7%68%95%

A normal curve with horizontal axis labeled "Mean G P A" from less than 2.99 to 3.41 plus in intervals of 0.07 is centered at 3.2. The area below the curve is subdivided into three labeled regions by three pairs of solid vertical lines that extend from the horizontal axis to the normal curve with horizontal coordinates as follows: 3.13 to 3.27, 68%; 3.06 to 3.34, 95%; 2.99 to 3.41, 99.7%.

B.

2.152.52.853.23.553.94.25MeanGPA99.7%68%95%

A normal curve with horizontal axis labeled "Mean G P A" from less than 2.15 to 4.25 plus in intervals of 0.35 is centered at 3.2. The area below the curve is subdivided into three labeled regions by three pairs of solid vertical lines that extend from the horizontal axis to the normal curve with horizontal coordinates as follows: 2.85 to 3.55, 68%; 2.5 to 3.9, 95%; 2.15 to 4.25, 99.7%.

C.

-3-2-10123MeanGPA99.7%68%95%