Name: Homework Assignment Six Due Friday, Feb. 27 th

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Laurence Elvin Morgan
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1 Name: Homework Assignment Six Due Friday, Feb. 27 th Suggest Reading: Chapter 5 Section 1 3, Chapter 6 Section 1- Section 2 1. List the probability model for the below situations. (Remember to list the entire sample space and then to list the probabilities for each of the events in the sample space.) a.) Roll a six sided dice and record the outcome on the dice. b.) Roll a six sided dice and record whether it is odd or even. c.) Stand at the end of an off ramp and record whether each car goes right or left. (They can t go straight.) Assume that the probability that the driver turns right is 0.45 and the probability that the driver turns left is A consumer organization estimates that over a 1 year period, 20% of cars will be repaired once, 35% will have only an oil change, 15% will be required to have multiple repairs and 30% will not be touched by a mechanic. Each of these events are disjoint. Repaired Once Had An Oil Change Repaired multiple Times X a.) What is the probability that a car is repaired once or multiple times? Not touched by a mechanic b.) What is the probability that a car is does not have an oil change? c.) What is the probability that the car either had an oil change or was not touched by a mechanic?

2 3. Upon reviewing recent usage of conference rooms at an engineering consulting firm, an industrial engineer determined the following function for the number of requests for a conference room per half day. The function is listed below. X probability a.) Is this a legitimate probability distribution function? b.) What is the probability that X is greater than 1? c.) What is the probability that X is greater than or equal to 1? d.) What is the probability that X is greater than 2? e.) What is the probability that X is greater than 5? f.) What is the probability that X is 3? g.) Find the mean. h.) Draw a probability histogram.

3 4. Someone created a probability distribution where X is the number of lights stopped on 13 th Street on a typical morning between NW 39 th Avenue and University Avenue. X probability a.) Is this a legitimate probability distribution? Why? 5. Someone else created a probability distribution where X is the number of repair calls for telephones on campus per day. X probability a.) Is this a legitimate probability distribution? Why? 6. Below is the result of a 2012 General Social Survey question about whether or not the respondent had ever been divorced. Divorced Not divorced Total Male Female Total a.) What is the conditional probability that a male has been divorced? b.) What is the conditional probability that someone is divorced given that they are male? c.) What is the conditional probability that someone that is divorced is female? d.) What is the conditional probability that someone is divorced given that they are female? e.) What is the conditional probability that some that is divorced is male?

4 7. Below is the result of a 2012 General Social Survey question about volunteering in the past month based on their gender. Yes, have No, have not Total volunteered volunteered Male Female Total a.) What is the conditional probability that a male has volunteered in the past month? b.) What is the conditional probability that female has volunteered in the past month? c.) What is the conditional probability that someone that has volunteered in the past month is male? d.) What is the conditional probability that someone that has volunteered in the past month is female? e.) What is the probability that someone has volunteered in the past month?

5 8. Below is the result of a 2008 General Social Survey question about health insurance based on their political party. Only individual employees are covered Employees and their spouses are covered, but domestic partners are not covered. Employees and their spouses are covered as well as domestic partners are covered. Democrat Republican Independent Total Total a.) What proportion of the sample were Democrats? b.) What proportion of the sample had only individual employee health insurance coverage? c.) What proportion of Democrats had only individual employee health insurance coverage? d.) What proportion of those that have health coverage for employees and spouses, but not domestic partners are Republicans? e.) What is the proportion of those that only receive individual insurance coverage, given that they are Independents? f.) What is the proportion of Republicans that have health insurance coverage for themselves, their spouses as well as their domestic partners?

6 9. For 2012, the ACT Math portion scores are normally distributed with a mean of 21.1 and a standard deviation of 4.2. a.) Draw a graph of this distribution with the mean and the change of curvature points. b.) Using the graph above, what percentage of people has ACT scores between 16.9 and 25.3? c.) Using the graph above, what percentage of people have ACT scores between 12.7 and 29.5? d.) Using the graph above, what percentage of people have ACT score between 8.5 and 33.7?

7 10. For 2012, the ACT Math portion scores are normally distributed with a mean of 21.1 and a standard deviation of 4.2. a.) John makes a 25 on the test. What is his z-score? b.) What percentage of students scores less than 25? (List the distribution, the population mean and the population standard deviation. Draw a picture, show the calculator code and write a sentence explaining the answer.) c.) What score would John need to make to be at the 97 th percentile? (List the distribution, the population mean and the population standard deviation. Draw a picture, show the calculator code and write a sentence explaining the answer.)

8 11. For 2012, the ACT Math portion scores are normally distributed with a mean of 21.1 and a standard deviation of 4.2. d.) Jane makes a 19 on the test. What is her z-score? e.) What percentage of students scores less than 19? (List the distribution, the population mean and the population standard deviation. Draw a picture, show the calculator code and write a sentence explaining the answer.) f.) What score would Jane need to make to be at the 85 th percentile? (List the distribution, the population mean and the population standard deviation. Draw a picture, show the calculator code and write a sentence explaining the answer.)

9 12. problem 6.4 page 275 a.) b.) 13. problem 6.26 on page 287 (List the distribution, the population mean and the population standard deviation. Draw a picture, show the calculator code and write a sentence explaining the answer.) a.) b.) c.)

AP Stats ~ Lesson 6B: Transforming and Combining Random variables

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