1. Briefly, what is probability (include in this the 3 "approaches" to probability discussed in your reading material).
2. Please (1) work the following problems, (2) tell me what rule or principle you used to solve them and (3) then look at others' answers to check yourself and that person -- let's see if we can come to consensus on them!
Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at graduation.
a. What is the probability both of the selected students plan to attend college?
b. What is the probability one of the two selected students plans to attend college?
3. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:
Gender Major Accounting Management Finance total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500
a. What is the probability of selecting a female student?
b. What is the probability of selecting a finance or accounting major?
c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
d. Are gender and major independent? Why?
e. What is the probability of selecting an accounting major, given that the person selected is a male?
f. Suppose two students are selected randomly to attend a lunch with the president of the university. What is the probability that both of those selected are accounting majors?
4. Reynolds Construction Company has agreed not to erect all "look-alike" homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the exterior and interior plans be offered to potential home buyers?
5. A puzzle in the newspaper presents a matching problem. The names of 10 in one U.S. presidents are listed column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president. If you make the matches randomly, how many matches are possible? What is the probability all 10 of your matches are correct?
6. Convert each category into probabilities:
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Class Interval
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Frequencies
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Probabilities
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6 to 10 minutes
|
3
|
|
|
11 to 15 minutes
|
8
|
|
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16 to 20 minutes
|
6
|
|
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21 to 25 minutes
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2
|
|
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More than 25 Minutes
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1
|
|
Using your probability distribution above, answer the following:
1. An oil change shop advertised to change oil within 15 minutes. Based on the data collected on a typical day, what is the probability that oil change will take 15 minutes or less time?
2. Based on the data, do you think the business claim is valid? Explain why or why not.
7. When conducting an experiment, if the number of trials and the long run probability of success are known and each trial is independent of the others, the probabilities for each possible outcome of the experiment will follow a particular distribution of probabilities called the Binomial Probability Distribution. This type of discrete probability distribution is discussed in Chapter 6 in the Lind text. Binomial probability distributions can be generated using Excel or you can use Appendix B-9 from the Lind text. Use this material to address the following:
Let's assume at the intersection of Canyon Road and 20th Street there is a traffic light. You have been told that the city engineers have set the light to red 40% of the time. You approach the light from the east 8 random times during this experiment. What is the probability of the light being red:
1. Exactly 4 times?
2. 4 times or more?
3. Less than 3 times?
4. What is the expected number of times the light will be red?
8. How does the Empirical Rule apply to continuous discrete probability distributions? Does the Empirical Rule always apply to discrete probability distributions? Why or why not?