MATH 227 CP 6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 MATH 227 CP 6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the given random variable as being discrete or continuous. 1) The number of phone calls between New York and California on Thanksgiving day 1) 2) The ph level in a shampoo 2) Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. 3) 3) ) ) 5) ) 6) A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.122, 0.257, 0.270, 0.189, and 0.099, respectively. 6) Find the mean of the given probability distribution. 7) ) 1

2 8) The number of golf balls ordered by customers of a pro shop has the following probability distribution ) 9) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are , , , , and , respectively. Round answer to the nearest hundredth. 9) 10) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.54, 0.43, 0.02, and 0.01, respectively. 10) Provide an appropriate response. Round to the nearest hundredth. 11) Find the standard deviation for the given probability distribution ) 12) In a certain town, 70% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution ) 13) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.46, 0.41, 0.09, and 0.04, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth. 13) Answer the question. 14) Focus groups of 12 people are randomly selected to discuss products of the Famous Company. It is determined that the mean number (per group) who recognize the Famous brand name is 7, and the standard deviation is Would it be unusual to randomly select 12 people and find that greater than 10 recognize the Famous brand name? 14) 15) Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games? 15) 2

3 16) Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are considered morbidly obese. Is it unusual to have no obese subjects among three randomly selected adolescents? ) Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls) P(x) x(girls) P(x) ) Find the probability of selecting 12 or more girls. 17) 18) Find the probability of selecting exactly 8 girls. 18) 19) Find the probability of selecting 9 or more girls. 19) 20) Find the probability of selecting exactly 4 girls. 20) 21) Find the probability of selecting 2 or more girls. 21) 22) Find the probability of selecting exactly 5 girls. 22) Provide an appropriate response. 23) In a game, you have a 1/36 probability of winning $85 and a 35/36 probability of losing $4. What is your expected value? 23) 24) A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $8000 with a probability of 0.3. What is the expected profit? 24) 25) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 or a 3, nothing otherwise. What is your expected value? 25) 26) The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $4200 (1 chance in 8000); $1600 (1 chance in 6900); $500 (1 chance in 3300); $300 (1 chance in 2000). Find the expected value of the amount won for one entry if the cost of entering is 53 cents. 26) 3

4 27) A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is , what is the expected value for the insurance policy? 27) 28) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? 28) Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 29) Rolling a single die 53 times, keeping track of the "fives" rolled. 29) Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 30) n = 10, x = 2, p = ) 31) n = 64, x = 3, p = ) 32) n = 7, x = 4, p = ) Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 33) Choosing 4 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time 33) without replacement, keeping track of the number of red marbles chosen. Find the indicated probability. Round to three decimal places. 34) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority? 34) 35) A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? 35) 36) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? 36) Find the indicated probability. 37) The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name. 37) 38) A company manufactures calculators in batches of 55 and claims that the rate of defects is 5%. Find the probability of getting exactly 3 defects in a batch of 55 if the rate of defects is 5%. If a store receives a batch of 55 calculators and finds that there are 3 defective calculators, do they have any reason to doubt the company's claimed rate of defects? 38) 4

5 39) A slot machine at a hotel is configured so that there is a 1/1200 probability of winning the jackpot on any individual trial. If a guest plays the slot machine 6 times, find the probability of exactly 2 jackpots. If a guest told the hotel manager that she had hit two jackpots in 6 plays of the slot machine, would the manager be surprised? 39) 5

6 Answer Key Testname: MATH227CP6 1) Discrete 2) Continuous 3) Not a probability distribution. The sum of the P(x)'s is not 1, since ) Probability distribution. 5) Not a probability distribution. One of the P(x)'s is negative. 6) Not a probability distribution. The sum of the P(x)'s is not 1, since ) µ = ) µ = ) µ = ) µ = ) = ) = ) = ) Yes 15) Yes 16) No 17) ) ) ) ) ) ) -$ ) $15,800 25) -$ ) $ ) -$ ) -$ ) Procedure results in a binomial distribution. 30) ) ) ) Not binomial: the trials are not independent. 34) ) ) ) ) 0.228; No. If the rate of defects is really 5%, it is not so unlikely to find 3 defects in a batch of 55 calculators. 39) ; Yes, the probability of 2 jackpots in 6 plays is extremely small. 6

Problem Set 07 Discrete Random Variables

Name Problem Set 07 Discrete Random Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the random variable. 1) The random