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# Probability Statements and Regression Data

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3. Spring-loaded canons are designed to shoot t-shirts into the stands at sporting events. Test firings are conducted on a large level field. The distance that a t-shirt flies is a function of the angle of elevation. When the angle is 35 degrees, the distances follow a normal distribution with a mean of 114.0 feet and a standard deviation of 8.0 feet.

a. At 35 degree of elevation angle what proportion of shots will be longer than 118 feet?
Show all work. Draw a picture.
Include an appropriate probability statement with your answer on the line to the right.
______________________

b. Calculate the distance such that at 35 degrees elevation 8% of all shots will exceed this distance?
Show all work. Draw a picture. Include an appropriate probability statement with your answer.
______________________

c. If 16 shots were fired at 35 degrees elevation, what is the probability that the sample mean would be less than
118 feet? Show all work. Draw a picture. Include an appropriate probability statement with your answer.
______________________

4. A random sample of Fortune 500 companies was selected. The companies were grouped
by industry, then a proportion of each industry was selected. A model was developed
for estimating assets.

a. What type of sampling is this called? ________________

A regression model is being developed to estimate the mean assets of a company
based on values of several other of its characteristics. The Minitab results follow:
Predictor Coef SE Coef T P
Constant 2543.9 821.3 3.10 0.003
Sales 1.4708 0.3463 4.25 0.000
Market_Value 0.6277 0.2908 2.16 0.034
Profits -6.890 6.935 -0.99 0.324
Employees -91.26 26.97 -3.38 0.001

S = ___________? R-Sq = ____________?

Analysis of Variance

Source DF SS MS F P
Regression 4 4200852404 ___________ 26.22 0.000
Residual Error 73 2339189779 32043696
Total ___ 6540042184

b. Fill in the four blanks above.

c. How many predictor variables are used in the current model? ___________

d. What proportion of the variation of the assets can be accounted for by using this set of variables in the above regression? ___________

e. Which variable should the first candidate for elimination? Give the name from above. ____________
Should it be eliminated? (Yes or No) ________

f. Write the least squares prediction equation.

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#### Solution Preview

Please see the attachments.

Spring-loaded canons are designed to shoot t-shirts into the stands at sporting events. Test firings are conducted on a large level field. The distance that a t-shirt flies is a function of the angle of elevation. When the angle is 35 degrees, the distances follow a normal distribution with a mean of 114.0 feet and a standard deviation of 8.0 feet.

a. At 35 degree of elevation angle what proportion of shots will be longer than 118 feet?
Show all work. Draw a picture.
Include an appropriate probability statement with your answer on the line to the right.

Answer
Let X be the distance that a t shirt flies. Given that X is normal with mean µ 114 and standard deviation σ = 8.

We need P(X>118). Standardizing the variable using and from standard normal table we have = P(Z>0.50) =0.6915

Probability for X >118
X ...

#### Solution Summary

This solution analyzes the two questions and shows step-by-step calculations and explanations to determine the probability statements with annotated diagrams. It also provides a regression model to estimate the mean and other statistical data.

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