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aleksley [76]
3 years ago
13

A university is conducting a survey to study the number of hours students sleep at night during exam week. A sample of 20 studen

ts was drawn, and these responses were obtained: 6.5, 5, 8, 5.5, 7, 4, 4.5, 5, 6, 5.5, 4, 7.5, 6, 7, 8, 5, 6, 6.5, 6.5, 5. The standard deviation of the population mean is 2 hours. Arrange the steps in the correct sequence to find the range in which 95% of the sample mean occurs. Tiles The standard error of the mean of the sample is . The range in which 95% of the sample mean occurs is . The range in which 95% of the sample mean occurs is 5.93 + 2 × 0.45 = 6.83 hours and 5.93 − 2 × 0.45 = 5.03 hours. The sample mean is . The 20 students' total number of study hours is 118.5 hours. Calculate the standard deviation.
Mathematics
1 answer:
Ronch [10]3 years ago
4 0
1. To calculate the mean, we first total the number of hours: The 20 students' total number of study hours is 118.5 hours.
2. We divide by the number of samples to find the mean: <span>The sample mean is 5.93.</span>
3. Next, we find the SD: <span>Calculate the standard deviation.</span>
4. Then we divide SD by the number of samples to get the standard error: the standard error of the mean of the sample is 0.45.
5. Since for a 95% CI, the corresponding z-score is 1.96 ~ 2, we use the formula for CI: mean +/- z*SE, which is: The range in which 95% of the sample mean occurs is 5.93 + 2 × 0.45 = 6.83 hours and 5.93 − 2 × 0.45 = 5.03 hours.
6. Finally: The range in which 95% of the sample mean occurs is (5.03, 6.83).
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It will take 39.27 gallons to repaint the barn.

Step-by-step explanation:

The image of the setup is obtained from online and attached to this solution.

The rectangular prism is a cuboid of

Length = 84 ft

Breadth = 38 ft

Height = 20 ft

And the triangular prism on top of the rectangular prism has a vertical height of 12 ft.

The surface area of the composite structure that is available for painting include the 4 sides of the top triangular prism and the four sides of rectangular prism

Two of the faces of the triangular prism are triangles with base of 38 ft and height of 12 ft.

The other two faces of the triangular prism are rectangles with length 84 ft and breadth of the hypoteneuse of the right angled triangle on top.

B² = 12² + 19²

B = 22.47 ft

Total Surface area of the faces of the rectangular prism is then

2×(84×20) + 2×(38×20) = 4880 ft²

Total surface area of the faces of the triangular prism is then

2×(0.5×12×38) + 2×(84×22.47) = 4,230.96 ft²

Total surface area = 4880 + 4230.96 = 9110.96 ft²

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