[meteor_slideshow slideshow=”arp1″]
1. Consider a random number generator that produces only 1’s and 2’s (i.e. X= 1,2 for all N).
(a) What is the mean, µ, and variance, ∂2 of this distribution for samples of size 1?
(b) For samples of size 3, i.e. n = 3, there will be how many distinct sampling outcomes?
(c) Construct the sampling distribution of Xbar for n = 3.
(d) What is the mean and variance of this sampling distribution?
(e) Consider the sampling distribution for samples of size 9, what is the mean and standard deviation of this sampling distribution?
2. The revenue and cost functions for producing and selling quantity x for a certain company are given below.
R(x) = 12x – x2
C(x) = 21 + 2x
(a) Determine the profit function P(x).
(b) Compute the break-even quantities.
(c) Determine the average cost at the break-even quantities.
(d) Determine the marginal revenue R’(x).
(e) Determine the marginal cost C’(x).
At what quantity is the profit maximized?
3. A store wishes to predict net profit as a function of sales for the next year. The following table gives the years 1998 to 2005.
Year
Sales
(thousands of dollars)
Net Profit
1998
48
8.0
1999
52
9.4
2000
53
11.3
2001
78
8.6
2002
80
6.6
2003
70
4.1
2004
62
−1.0
2005
55
−2.0
(a) Graph the points from 1998 through 2005 on a scatter diagram using Sales as the independent variable and Net Profit as the dependent variable.
(b) Discard the obvious outliers and compute the least squares regression line using the remaining data.
(c) Draw the regression line on the graph you constructed in Part (a).
(d) What is the predicted net profit for 2006 if sales are expected to be 75?
(e) What is the correct t-score if you were to calculate a 95% prediction interval estimate?
(f) Calculate the standard error of estimate, Se, for the data.
(g) Find the 95% prediction interval estimate.
(h) What is the value of the coefficient of determination for this regression model?
Predict the net profit using the regression line at the zero sales level.
4. A newspaper vendor is trying to decide how many newspapers to order for each day. Any newspapers not sold during the day are thrown away. He buys each newspaper for 75 cents and sells it for a dollar. The following demand distribution has been observed in the past.
Demand
(Number of Newspapers)
Relative Frequency
50
0.10
60
0.20
70
0.40
80
0.20
90
0.10
The vendor would like to evaluate policies of ordering 60 and 80 newspapers each day.
(a) Simulate each policy for 6 days.
Which policy gives a higher profit?
[meteor_slideshow slideshow=”arp2″]
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