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.
See attachment for a better representation.
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.