Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Week-in-Review 8 Problem Set1. For the following random variables, list the values that X can assume and state whether it isfinite discrete, infinite discrete, or continuous.(a) Let X be the number of times it takes for you to hit the bull’s eye while playing darts.(b) Let X be the amount of water (in liters) that a person drinks each week.(c) Cards are drawn from a standard deck of cards with replacement until a king is drawn.Let X be the number of draws needed.(d) Bingo numbers are pulled out of a bag without replacement until B1 is called. Let X bethe number of pulls needed. (There are 75 total bingo numbers.)(e) Three marbles are pulled in succession with replacement from a jar containing 3 red, 4blue, and 5 green. Let X be the number of blue marbles pulled.(f) Let X be the distance (in miles) between College Station and a student’s hometown.2. Two 4-sided die are rolled and the numbers are observed. Let X be the product of the numbersrolled.(a) Find the sample space for this experiment.(b) What values can X take on?(c) Find the probability distribution for X.(d) Draw a histogram of this distribution.(e) What is P (X ≥ 8)?3. In a bag of 20 Starbursts, it is known that 7 are orange. A sample of 5 Starbursts are selectedat random from the bag. Let X be the number of oranges selected.(a) Find the probability distribution of X.(b) Draw a histogram for X.(c) What is P (X < 3)?(d) Find the expected value of X.(e) What are the variance and standard deviation for this probability distribution?4. (Modified from Finite Mathematics by Waner/Costenoble) Data is given below showing the number of cars that areof a certain age (in years). The data was taken from a study of 2000 cars on a universitycampus.Age of Car 0 1 2 3 4 5 6 7 8 9 10Number of Cars 140 350 450 650 200 120 50 10 5 15 10(a) Find the mean, median, mode, variance, and standard deviation for the age of a car onthis campus.(b) Let X be the age of a randomly selected car. Find the probability distribution for X.1Math 141 WIR, Spring 2007,cBenjamin Aurispa5. Suppose the probability that a person likes pizza is 0.73.(a) What are the odds that this person likes pizza.(b) What are the odds that this person does NOT like pizza?6. A gambler wants to bet on a horse race. There are 6 horses entered in the race. The odds ofeach horse winning are given below.Horse A B C D E FOdds 1 to 19 2 to 3 1 to 3 3 to 17 1 to 9 1 to 19(a) Suppose the gambler places a $20 bet on Horse B. If Horse B wins the race, the gamblergets $45. Otherwise, he wins nothing. What are the expected net winnings for thegambler?(b) Suppose the gambler places a $30 bet on Horse A. If Horse A wins the race, the gamblergets $150. Otherwise, he wins nothing. What are the expected net winnings for thegambler?(c) Suppose the gambler wants to place a bet on Horse E. He knows that if Horse E wins,he will get an amount of money equal to 3 times his bet plus an extra $140. How muchshould he bet so that this “game” would be considered fair?7. A game at a carnival costs $4 to play. The game consists of first tossing a coin. If a tail istossed, the game is over and you win nothing. If a head is tossed, then a tile is selected froma bag of tiles filled with a tile for every letter of the alphabet. If a vowel is selected, you win$15. If w is selected, you win $40. If l, m, or n is selected, you win $5. If the dreaded x isselected, you have to pay an extra $1. Otherwise, you win nothing. What are the expected netwinnings for a person who plays this game? Is this game fair?8. A car insurance policy covers damages from a car accident. If you get in a wreck. the insurancecompany pays out $1500.(a) Suppose your monthly payment is $110 and the probability that you get in a wreck is0.05. What is the insurance company’s expected gain?(b) Suppose that you provide an extra risk to the insurance company because the probabilitythat you get in a wreck is 0.15. If the insurance company requires an expected gain thatis greater than or equal to 0, what would be your minimum monthly payment?Note: The following problem requires the use of Chebychev’s Inequality, which some instructorsmay not cover.9. A random variable X has expected value 34 and a standard deviation of 6. Estimate theprobability that a randomly chosen outcome of the experiment lies between 10 and
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