During the first week of January a department store allows c

During the first week of January, a department store allows customers to spin a wheel that points to either a 25% discount, a 10% discount, or no discount after it stops. The wheel is constructed so that the chance of getting a 25% discount is 10%, the chance of getting a 10% discount is 25%, and the chance of getting no discount is 65%.
On average, what percent discount can customers expect to receive?

A. 12.5%

B. 17.5%

C. 5%

D. 2.5%

E. 7.25%

A researcher was conducting a study of a variety of pine trees. Collecting data, he performed a regression analysis and found that the circumference (in inches) of the tree was linearly related to the height (in feet) of the tree. Based on the analysis, the following represents the best-fit straight line through the data.

Circumference = 6.78 + 0.272 x Height 10 ft

Measuring a particular tree, he found that the circumference was 19.7 inches. Based on the regression, which of the following represents the best estimate of the tree\'s height?

A. 54.5 FT

B. 25.6 ft

C. 34.8 ft

D. 47.5 ft

E. 19.2 ft

Solution

1)

Option C 5%

Break it into 20 pieces (2 @ 25%, 5@ 10% and 13 at 0%). When you do a weighted average you get 5%

(a) (b) (a)*(b)
25.00% 5.00% 1.25%
25.00% 5.00% 1.25%
10.00% 5.00% 0.50%
10.00% 5.00% 0.50%
10.00% 5.00% 0.50%
10.00% 5.00% 0.50%
10.00% 5.00% 0.50%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
0.00% 5.00% 0.00%
100.00% 5.00%

2)

Option D ) 47.5 ft

Circumference = 6.78 + 0.272 x Height 10 ft

=>19.7= 6.78 + 0.272 * H

=> H = (19.7-6.78)/0.272 = 47.5