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TAMU MATH 141 - 141wir9ws

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Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Exam 3 Review Problem SetNote: Not every topic is covered in this review. It is more heavily weighted on 8.4-8.6. Please alsotake a look at the previous Week in Reviews for more practice problems on other sections.1. Determine whether the following experiments are binomial.(a) Picking 3 cards in succession with replacement from a deck of cards and observing if thecard is a king.(b) Tossing a coin until a head is tossed.(c) Rolling a pair of dice 5 times and recording the sum.(d) Picking 4 marbles in succession without replacement from a jar of 3 red and 5 blue marblesand observing the color of the marble.2. A certain medicine is known to cause nausea in 35% of those who take it. In a group of 15people who are taking this medicine, what is the probability that:(a) Exactly 7 of them will have nausea?(b) At most 5 of them will have nausea?(c) At least 9 will have nausea?1Math 141 WIR, Spring 2007,cBenjamin Aurispa3. Suppose a biased coin is tossed 400 times. The coin is biased such that the probability oftossing a head is .70. What is the probability that(a) Exactly 275 heads are tossed?(b) More than 300 heads are tossed?(c) 293 or fewer heads are tossed?(d) What is the expected number of heads that will be tossed?(e) What are the variance and standard deviation for the number of heads tossed?4. Calculate the following probabilities. (Z is the standard normal random variable.)(a) P (−0.33 < Z < 0.47)(b) P (Z < 0.93)(c) P (Z > 0.29)2Math 141 WIR, Spring 2007,cBenjamin Aurispa5. Find the value of z that satisfies the following probabilities.(a) P (Z < z) = 0.3682(b) P (Z > z) = 0.9778(c) P (−z < Z < z) = 0.52546. Suppose that the weights of students at a university are normally distributed with a mean of165 and a standard deviation 24. What is the probability that a student selected at random(a) weighs between 150 and 200 pounds?(b) weighs more than 215 pounds?3Math 141 WIR, Spring 2007,cBenjamin Aurispa7. The government of a certain country wants to create a system for tax purposes where familiesare classified as “elite,” “upper class,” “middle class,” or “lower class” based on the totalfamily income. Suppose family incomes in this country are normally distributed with a meanof $30,000 and a standard deviation of $9,000. If this government knows that they want 15%elite, 25% upper class, 40% middle class, and 20% lower class, what would be the range ofincome classified as “middle class?”8. Suppose the probability that Acie Law makes a 3-pointer is 0.64 and that he attempts 400 3-pointers during his career. Use an appropriate normal distribution to approximate the followingbinomial probabilities.(a) What is the probability that Acie makes between 250 and 300 3-pointers (inclusive)?(b) What is the probability that Acie makes at least 230 3-pointers?(c) What is the probability that Acie makes fewer than 260 3-pointers?4Math 141 WIR, Spring 2007,cBenjamin Aurispa9. A toy chest contains 9 Micro Machines, 7 Lego blocks, and 4 GI Joes. Suppose that 6 toys areselected at random from the box. What is the probability that(a) exactly 4 Lego blocks and exactly 2 GI Joes are selected?(b) exactly 3 Micro Machines or exactly 2 Lego blocks are selected?(c) at least 1 GI Joe is selected?10. Suppose that 59% of students at Texas A&M listen to country music. It is known that 37% ofthose who listen to country music attended Chilifest while 26% of those who do not listen tocountry music attended Chilifest.(a) What is the probabilty that a student does not listen to country music and did not attendChilifest?(b) What is the probability that a student who listens to country music did not attendChilifest?(c) Are the events “listens to country music” and “attended Chilifest” independent events?5Math 141 WIR, Spring 2007,cBenjamin Aurispa11. A bag of jelly beans contains 7 whites and 10 oranges. An experiment consists of picking ajelly bean at random. If the jelly bean is white, it is immediately eaten and a second jelly be anis picked from the bag. If the jelly bean is orange it is put back into the bag and a second jellybean is picked from the bag. What is the probability that the first jelly bean is white giventhat the second jelly bean is orange?12. A lie detector correctly indicates that a person is lying 94% of the time. However, 11% of thetime, the test incorrectly indicates that a person is lying when they really aren’t. A group ofstudents are asked “Do you like math?” while hooked up to a lie detector. It is known that45% of these students are actually lying. If the test says a person is not lying, what is theprobability that the person really is?6Math 141 WIR, Spring 2007,cBenjamin Aurispa13. A game costs $3 to play. The game involves drawing two cards at random from a deck ofcards. If a pair of aces is drawn, you win $38. If any other pair is drawn, then you win $13.If two cards of the same suit are drawn, you win $8. Otherwise, you win nothing. What arethe expected net winnings of a person who plays this game. Is this game fair? What are thestandard deviation and variance for the net winnings?14. There are 130 boxes of Cheerios in a groc ery store. The following table tells you how manyboxes had a certain number of Cheerios in them.Number of Cheerios 510 480 467 434 521 535Number of boxes 23 40 17 30 9 11(a) Find the mean, median, mode , standard deviation, and variance for the number of Cheeriosin a box.(b) Find the probability distribution of X where X is the number of Cheerios in a box.(c) What is P (X > 500)?7Math 141 WIR, Spring 2007,cBenjamin Aurispa15. Determine whether the following statements are True or False:(a) TRUE FALSE An experiment consists of rolling a die 4 times. Let X be the sum ofthe numbers rolled. X is a finite discrete random variable.(b) TRUE FALSE An experiment consists of drawing cards without replacement from astandard deck until all four Aces have been drawn. Let X be the number of draws needed.X can be any value in the set {1, 2, 3, . . . , 52}.(c) TRUE FALSE A bag of marbles contains 5 reds and 6 blues. An expe riment consistsof pulling marbles out in succession with replacement until a red marble is pulled. Let Xbe the number of pulls needed. X is an infinite discrete random variable.(d) TRUE FALSE Let X be the amount of time (in hours) it takes a person to drive towork or school every day. X is an infinite discrete random variable.(e) TRUE FALSE If the


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