Quiz 5

MATH106 – 6380

Quiz 5

Directions:

• Read and sign the academic honesty certification statement below, then read the questions carefully and answer them to the best of your ability. You may write your answers on this sheet or on the sheet you do your work on, but PLEASE show your work. Answers shown without work will get no credit. Work shown with unclear derivations or key steps missing in the derivations of answers will not lead to full credit (even if the answer is correct). Follow directions as outlined in Quizzes folder under the “Assignments” link on our LEO classroom NavBar.

• The completed quiz that you submit/upload must be contained in one file (Word or .pdf format). Uploaded work in other formats or separated over more than one file will not be accepted.

• Test & work is due as specified in “Course Schedule”. I cannot accept any late submissions! This is open-book/notes: calculators, & graphing devices are authorized for use. Good luck!

Show your work!

• Evaluate manually and write/type it on the quiz document, or

• Provide scan/image of work done on calculator or other software, or

• Insert chart/graphic if using software that produces such objects.

Show your work!

• Evaluate manually and write/type it on the quiz document, or

• Provide scan/image of work done on calculator, or

• Insert chart/graphic if using software

1. Evaluate:

a. 11 P 5 ___________________

b. 11 C 5 ___________________

2. What is the probability of someone correctly guessing your Social Security number on the first attempt? (Assume all digits 0-9 are available for use) (Hint: does order matter?)

Answer: _____________________________

3. A jar contains 7 red, 9 white, and 8 blue marbles. If a single marble is chosen at random, find the probability that the randomly chosen marble is:

1. Red ______________

1. White ______________

1. Blue OR red ______________

4. Multiple Choice: An assembly plant produces 40 lawn mowers; of those, 7 are defective. Prior to shipping the mowers to retailers, the company’s quality control department selects 10 of the 40 mowers at random for testing. The assembly plant will be shut down for troubleshooting if 1 or more mowers in the sample are found to be defective. What is the probability that the plant will be shut down? Justify your answer.

Hint: find the complementary probability that 0 of the 10 lawn mowers selected out of the production lot of 40 (with its 7 defective mowers) are defective. The probability that plant shuts down if 1 or more mowers in sample are found defective: .

1. C.

2. D.

Answer: ___________

5. The following table shows the 2015 distribution of U.S. Senators by political party and gender:

For a single Senator selected at random, use the table to find the following:

1. Probability that Senator is male and a Democrat: = _________

1. Probability that Senator is male or a Democrat: = _________

1. Probability that Senator is male given that he is a Democrat: = _________

1. Are the events “Females” and “Republicans” mutually exclusive? Using probability techniques, explain your answer. “Yes” or “No” answers without explanation, even if correct, receive no credit.

6. From a survey involving 1000 university students, a market research company found that 610 owned laptops, 200 owned cars, and 125 owned cars AND laptops. If a student is selected at random, what is the empirical probability that the student owns neither a car nor a laptop?

Answer: _________________________________

7. Scam Industries’ ULTRON 360 (“U”) artificial intelligence (AI) computer program has a 45% probability of passing an analytics evaluation. Amalgamated Ripoff Company’s more expensive OMEGA (“Ω”) AI program has a 65% probability of passing the same evaluation. If these two events are independent, find the following probabilities.

1. P(both systems will pass the evaluation) = ________________

1. P(at least one of them will pass the evaluation) = ________________

8. A fair two-sided coin is tossed 6 times. What is the probability of tossing a “head” on the 6th toss, given that the 5 preceding tosses were also “heads”?

Answer: _________________________________

9. Our classmate Hasiba Stukes is now a highly successful marketing wizard! She’s making a marketing presentation to the board of Jussaynoe Pharmaceuticals, who want to sell the anti-math anxiety drug SHOVITALL™ to the public. Hasiba has two marketing plans she’s come up with for the board’s decision:

• Plan A : a marketing plan that nets $30 million if successful (probability 0.8) and will lose $6 million if unsuccessful (probability 0.2)

• Plan B : a marketing plan that nets $44 million if successful (probability 0.6) and will lose $10 million if unsuccessful (probability 0.4)

1. Construct an expected value payoff table for the two marketing plans A and B :

1. Determine the expected values of each marketing plan (show your work!!).

E(A) = ______________ E(B) = _______________

1. Based on the expected return, which of Hasiba’s marketing plans should be approved by the board?

Answer: ___________________________

10. Players of the “Zuper-Zillions” lottery in the country of Urkashizmein pay 1 bog for a ticket that lets them select 5 non-repeating numbers from 1 to 49 followed by one “Z-bolt” number between 1 and 30. The current “Zuper-Zillions” jackpot is a record 1,500,000,000 (1.5 billion) bogs. What is the probability of correctly guessing all 6 values with just one ticket? (Hint: order doesn’t matter)

Answer: _____________________________

11. The test scores for 10 students in Ms. Sampson's homeroom were 61, 67, 81, 83, 87, 88, 89, 90, 98, and 100. Complete the frequency table.

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