Statistics 1040 Summer 2009 Exam III NAME. Point score Curved Score

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1 Statistics 1040 Summer 2009 Exam III NAME Point score Curved Score Each question is worth 10 points. There are 12 questions, so a total of 120 points is possible. No credit will be given unless your answer in clearly explained and/or all calculations shown. Calculators are permitted, but note that many of the questions REQUIRE the answer in fractional form and some require you NOT to use the calculator. 1. For the following basic probability questions. Give the RULE used in the appropriate blank (BEFORE the question), for each of the following situations, using one of the following letters: a. Simple multiplication rule: P(A) * P(B) b. More complex multiplication rule: P(A) * P(B A) c. Simple addition rule: P(A) + P(B) d. More complex addition rule: P(A) + P(B) - something. e. Complement rule.. Use rule -- for cases such as the odds of flipping 5 heads in a row with a fair coin.. Use rule -- for cases such as the probability of finding a student who scored EITHER above 700 OR below 400 on the SAT.. Use rule --- for cases such as the chances of drawing a flush (5 cards of the same suit) in a 5-card deal.. Use rule -- for cases such as finding the probability of finding books which have EITHER the term "statistics" or the term "regression" as part of their title or description in the card catalog.. Use rule -- for cases such as those of rolling at least one double six in 24 rolls of a pair of dice. 2. Explain what the notation P(B A) means in option (b) of question 1, exactly what it would mean in the case or cases you applied it to. 3. Explain what the "something" means in option (d) of question 1, and exactly what it means in the case or cases you applied it to.

2 4. What is the chance of rolling at least one double 6 in 24 rolls of a pair of dice? Set up the problem as carefully as possible, using one of the rules above, but without using your calculator -- but be sure you set it up so that it takes the smallest possible number of calculator punches to solve. 5. A die (= one of a pair of dice) is rolled 6 times. Leave the answers as appropriate fractions (that is, don't use your calculator here). a. The chance that the first roll is an ace (one-spot) OR that the last roll is an ace is: b. The chance that the first roll is an ace (one-spot) AND the last roll is an ace is: c. The chance that the first card in the deck is an ace OR the last card is an ace is d. The chance that the first card in the deck is an ace AND the last card is an ace is 6. In question 5, how and why do your answers to (b) and (d) differ in terms of the rules employed?

3 7. The formula N! / k! (N - k)! is part of the binomial formula. True or false (and of course state and explain the correct answer fully if the statement or parts of the statement are false). a. The exclamation points mean that the formula is really, really important. b. The formula is used in counting the number of ways to get k heads in N tosses of a coin. c. The rest of the binomial formula involves adding the above formula to p * (1 - p), where p is the probability of heads. 8. Find the probability of getting exactly 3 heads in 8 tosses of a coin, if the coin is weighted so that the probability of heads is 0.6. Set up the problem AND use your calculator to give the answer to 4 decimal places.

4 9. An oil company thinks that there is a 40 percent chance (on the basis of the geological formations) that a well in a certain spot will hit substantial amounts of oil. They hire a geologist who drills test holes to be more certain; in the past, he has been right 70 percent of the time whether or not substantial amounts of oil are in a spot. If the geologist's tests indicate a substantial amount of oil, the oil company should: (a) Disregard the geologist, since he is right only a bit more often than not, and assume the real chance is still forty percent. (b) Conclude that there is a seventy percent chance of hitting substantial amounts of oil when they drill. (c) Revise their prior probability to somewhere between 40 and 70 percent. (d) Revise their prior probability to another value. The correct option is: Explain your answer, and give the exact revised probability HERE: Show your work below, setting up a table with OIL / NO OIL at the top, and the geologists indicator of substantial oil. (TESTS YES / TESTS NO) along the side.

5 10. A gambler is going to play roulette 25 times, putting a dollar on a SECTION BET covering numbers 13 through 24 each time (a section bet will cover 12 numbers --of the 38 numbers on the wheel -- and will pay 2 to 1, which means he wins 2 dollars if one of the 12 numbers comes up, and loses a dollar otherwise. Remember that the wheel also has ). We want to set up the simplest accurate box model of this, and are considering the following possibilities: Box A: [25 tickets labeled (2) and 25 tickets labeled (-1) ] Box B: [ 12 tickets labeled 1through 12, 12 tickets labeled 13 through 24, 12 tickets labeled 25 through 36, 2 tickets labeled 0 and 00] Box C: [ 12 tickets labeled (2) and 26 tickets labeled (-1)] Box D: [12 tickets labeled 1 and 26 tickets labeled 0] is the best choice. 11. The expected value of the gambler's winnings (or losings) after 25 plays is Show work below: The standard deviation of the correct box model is Explain below how we found this value: So the standard error of the winnings or losings after 25 plays is = Explain below:

6 12. There is a --- percent chance for the gambler to WIN more than $ 3 after 25 plays of the game. Explain carefully how you arrived at your answer; the attached tables will help.