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# Probability, Variability, Regression and Statistical Measures

I'm stuck can you help me, please explain your answers.

1) The following payoff table shows profits associated with a set of 3 alternative under 2 possible states of nature.

States A1 A2 A3
1 12 -2 8
2 4 10 5
Where S1is state of nature 1 A1 is action alternative 1
S2 is state of nature 2 A2 is action alternative 2
A3 is action alternative 3

Referring to table, if the probability of S1 is 0.4, then the probability of S2 is
(A) 0.4
(B) 0.5
(C) 0.6
(D) 1.0

2) A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample means and range for each day.

Day In- Minutes R
1 58.5 5.1
2 47.6 7.8
3 64.3 6.1
4 60.6 5.7
5 63.7 6.2
6 57.5 6.0
7 55.0 5.4
8 54.9 6.1
9 55.0 5.9
10 62.7 5.0
11 61.9 7.1
12 60.0 6.5
13 58.3 5.9
14 52.0 5.2

Referring to the table, suppose the analyst constructs an R chart to see if the variability in production times is in control. What is the center line of this R chart?
A) 4.8 (B) 6.0 (C) 6.9 (D) 7.1

3) Once the control limits are set for a control chart, one attempts to:
A) discern patterns that might exist in value over time (B) determine whether any points fall outside the control limits (C) both of the above (D) none of the above

4) A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a
A) payback period matrix (B) decision matrix (C) decision tree (D) payoff table .

5) A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the % of paper delivered on time for 10-day period and construct a p chart to see whether the % is too erratic.

Day Percentage of paper delivered on time
1 46
2 45
3 46
4 45
5 43
6 48
7 46
8 49
9 48
10 47

Referring to the above table, what is the numerical value of the lower control limit for the p chart?
(A) 0.920
(B) 0.911
(C) 0.815
(D)0.798

6) The following payoff matrix:

Event Probability Action A Action B
1 0.5 400 700
2 0.5 200 500

The coefficient of variation for Action A is:
(A) 12.8 %
(B) 33.3 %
(C) 133.33%
(D) 333.33 %

7) The control chart:
(A) focus on the time dimension of a system
(B) captures the natural vaiability in the system
(C) can be used for categorical, discrete, or continuous variables
(D) all of the above

8) Variation signaled by individual fluctuation or patterns in the data is called
(A) special or assignable causes
(B) common or change causes
(C) explained variation
(D) the standard deviation

9) Blossom's flowers purchases roses for sale for Valentine's day. The rose are purchased for \$10 a dozen and are sold for \$20 a dozen. Any roses not sold on Valentine Day can be sold for \$5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine Day: 100, 200, or 400 dozen roses, The number of a alternatives for the payoff table is:
(A) 2
(B) 3
(C) 4
(D) it cannot be determine from the information given.

10) A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic

Sample Day Number Favoring Incumbent
1 57
2 57
3 53
4 51
5 55
6 60
7 56
8 59

Referring to the table, which expression best characterizes the p chart?
(A) hugging the center line
(B) Cycle
(C) hugging the control line
(D) Individual outliers

11) A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the percentage of paper delivered on time for 10 day period and construct a p chart to see whether the percentage is too erratic

Day Percentage of Paper Delivered on time
1 46
2 45
3 46
4 45
5 43
6 48
7 46
8 49
9 48
10 47

Referring to table, what is the numerical value of the center line for the p chart
(A) 0.926
(B) 0.911
(C) 0.885
(D) 0.500

12) Which of the following is amoral of the red bead experiment?
(A) Variation is parts of the process
(B) only management can change the system
(C) it's the system that primarily determine performance.

#### Solution Summary

This solution contains step-by-step calculations to determine statistics and probability questions. It touches on the concepts of variability, coefficients and regression.

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