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# Probability Distribution for Graphical Analysis

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1. Graphical Analysis Are the events shown in the Venn diagram below mutually exclusive?

Please see the attachment for graph.

2. Decide if the events are mutually exclusive.
Event A: Roll a 6 on an ideal six-sided die.
Event B: Roll a 4 on an ideal six-sided die.
1
Use the table below to answer questions 3-7.
Nursing Majors The table below shows the number of male and female students enrolled in nursing at the University of Oklahoma Health Services Center for a recent semester. Find the specified probability.
Nursing Majors Non-Nursing Majors Total
Males 95 1015 1110
Females 700 1727 2427
Total 795 2742 3537
3. The student is male or a non-nursing major.
4. The student is female or a nursing major.
5. A student is not male or a nursing major.
6. The student is male or a nursing major.
7. Are the events "being male" and "being a nursing major" mutually exclusive?
Section 3.4
8. Perform the indicated calculation. 7C3
9. Experimental Group In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible? Use the information below to answer questions 10 and 11.
Area Code An area code consists of three digits.
10. How many area codes are possible if there are no restrictions?
11. How many area codes are possible if the first digit cannot be a one or a zero?
12. What is the probability of selecting an area code at random that ends with an odd
number if the first digit can't be 1 or zero?
Section 4.1
13. Determine if the random variable x is discrete or continuous. Explain your reasoning.
x represents the number of rainy days in the month of June in Portland, Oregon.
Use the frequency distribution below to answer questions 13-17.
DVDs The number of defects per batch of DVDs inspected.
Defects 0 1 2 3 4 5
Batches 95 113 87 64 13 8
14. Use the frequency distribution to construct a probability distribution.
2
15. What is the mean of the probability distribution?
16. What is the variance of the probability distribution?
17. What is the standard deviation of the probability distribution?
18. Interpret the results in the context of the real-life situation (See the interpretations in
examples 5-7 of the text for a reference showing how to do this.).
Section 4.2
Identifying binomial experiments. Use the information below to answer question
19.
Lottery A state lottery randomly chooses 6 balls numbered from 1 to 40. You choose
6 numbers and purchase a lottery ticket. The random variable represents the number
of matches on your ticket to the numbers drawn in the lottery.
Use the characteristics of the binomial distribution given below to answer questions
20-22
Suppose there is a binomial distribution with: n = 47 and p = 0:67
20. What is the mean of the binomial distribution?
21. What is the variance of the binomial distribution?
22. What is the standard deviation of the binomial distribution?
Use the characteristics of the binomial experiment below to answer questions 23-
25.
23. What is the probability that exactly 4 say their favorite cookie is oatmeal raisin?
24. What is the probability that at least 4 say their favorite cookie is oatmeal raisin?
25. What is the probability that less than 4 say their favorite cookie is oatmeal raisin?

See attached.

https://brainmass.com/math/probability/probability-distribution-graphical-analysis-387665

#### Solution Summary

The solution provides step by step method for the calculation of probabilities. Formula for the calculation and Interpretations of the results are also included.

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## The Attached word document contains solutions to 7 problems on the Normal Distribution and Break-even analysis.

QUESTIONS
1.
Katherine D'Ann is planning to finance her college education by selling Programs at the football games for State University. There is a fixed cost of \$400 for printing these programs, and the variable cost is \$3. There is also a \$1,000 fee that is paid to the University for the Right to sell these programs. If Katherine was able to sel1 programs for \$5 each, how many would she have to sell in order to break even?

2.
Katherine D'Ann, from Problem 1-17, has become concerned that sales may fall, as the team is on a terrible losing streak and attendance has fallen off. In fact, Katherine believes that she will sell only 500 programs for the next game. If it were possible to raise the selling price of the program and still sell 500, what would the price have to be for Katherine to break even by selling 500?

3.
Farris Billiard Supply sells all types of billiard equipment, and is considering manufacturing their own brand of pool cues. Mysti Farris, the production manager, is currently investigating the production of a standard house pool cue that should be very popular. Upon analyzing the costs, Mysti determines that the materials and labor cost for each cue is \$25, and the fixed cost that must be covered is \$2,400 per week. With a selling price of \$40 each, how many pool cues must be sold to break even? What would the total revenue be at this break-even Point?

4.
Mysti Farris (see problem 1-19) is considering raising the selling price of each cue to \$50 instead of \$40. If this were done while the costs remain the same, what would the new break-even point be? What would the total revenue be at this break-even point?

5.
Mysti Farris (see problem 1-19) believes that there is a high probability that 120 pool cues can be sold if the selling price is appropriately set. What selling price would cause the break-even point to be 120?

6.
A student taking Management Science 301 at East Haven University will receive one of the five possible grades for the course: A, B, C, D, or F. The distribution of grades over the past two years is as follows: (PLEASE SEE ATTACHMENT)

If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course?

7.
An industrial oven used to cure sand cores for a factory manufacturing engine blocks for small cars is able to maintain constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 450 F and a standard deviation of 25 F. Leslie Larsen, president of the factory, is concerned about the large number of defective cores that have been produced in the past several months. If the oven gets hotter than 475 F, the core is defective. What is the probability that the oven will cause a core to be defective? What is the probability that the temperature of the oven will range from 460 to 470 F?

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