Chapter 5 - Practice Problems 1 Identify the given random variable as being discrete or continuous. 1) The number of oil spills occurring off the Alaskan coast 1) A) Continuous B) Discrete 2) The ph level in a shampoo 2) A) Discrete B) Continuous SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. 3) 3) x P(x) 1 0.037 2 0.200 3 0.444 4 0.296 4) In a certain town, 60% 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. x P(x) 0 0.0256 1 0.1536 2 0.3456 3 0.3456 4 0.1296 4) Find the mean of the given probability distribution. 5) The random variable x is the number of houses sold by a realtor in a single month at the Sendsomʹs Real Estate office. Its probability distribution is as follows. Houses Sold (x) Probability P(x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 5) A) 3.35 B) 3.60 C) 3.40 D) 3.50 6) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.55, 0.43, 0.01, and 0.01, respectively. 6) A) 0.48 B) 0.25 C) 1.50 D) 1.03 1
Solve the problem. 7) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.48, 0.36, 0.14, and 0.02, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth. 7) A) 1.04 B) 0.61 C) 0.78 D) 1.05 8) The random variable x is the number of houses sold by a realtor in a single month at the Sendsomʹs Real Estate Office. Its probability distribution is as follows. Find the standard deviation for the probability distribution. Houses Sold (x) Probability P(x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 4.45 B) 6.86 C) 2.25 D) 2.62 8) 9) In a game, you have a 1/31 probability of winning $71 and a 30/31 probability of losing $9. What is your expected value? A) $11.00 B) $2.29 C) -$6.42 D) -$8.71 9) 10) A 28-year-old man pays $207 for a one-year life insurance policy with coverage of $70,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? A) -$206.88 B) -$165.00 C) $69,958.00 D) $42.00 10) 11) The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $4200 (1 chance in 8200); $1900 (1 chance in 5400); $600 (1 chance in 3800); $200 (1 chance in 2500). Find the expected value of the amount won for one entry if the cost of entering is 63 cents. 11) A) $0.47 B) $200 C) $0.51 D) $1.02 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) 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 12) Find the probability of selecting exactly 8 girls. 12) A) 0.000 B) 0.022 C) 0.122 D) 0.183 2
13) Find the probability of selecting 9 or more girls. 13) A) 0.122 B) 0.212 C) 0.001 D) 0.061 Answer the question. 14) Focus groups of 12 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 9.4, and the standard deviation is 0.64. Would it be unusual to randomly select 12 people and find that fewer than 6 recognize the Yummy brand name? 14) A) Yes B) No 15) 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 6.9, and the standard deviation is 0.70. Would it be unusual to randomly select 12 people and find that greater than 10 recognize the Famous brand name? 15) A) Yes B) No 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? x P x 0 0.111 1 0.215 2 0.450 3 0.224 A) Yes B) No 16) Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 17) Rolling a single ʺloadedʺ die 34 times, keeping track of the numbers that are rolled. 17) A) Not binomial: the trials are not independent. B) Not binomial: there are too many trials. C) Not binomial: there are more than two outcomes for each trial. D) Procedure results in a binomial distribution. 18) Rolling a single die 30 times, keeping track of the ʺfivesʺ rolled. 18) A) Procedure results in a binomial distribution. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: the trials are not independent. D) Not binomial: there are too many trials. 19) Choosing 5 people (without replacement) from a group of 23 people, of which 15 are women, keeping track of the number of men chosen. A) Procedure results in a binomial distribution. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: the trials are not independent. D) Not binomial: there are too many trials. 19) 3
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. 20) n = 4, x = 3, p = 1 6 20) A) 0.0116 B) 0.0231 C) 0.0039 D) 0.0154 21) n = 5, x = 2, p = 0.70 21) A) 0.132 B) 0.464 C) 0.700 D) 0.198 Find the indicated probability. 22) A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? 22) A) 0.0482 B) 0.9399 C) 0.5389 D) 0.1669 Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 23) n = 41; p =.2 23) A) μ = 8.2 B) μ = 7.7 C) μ = 8.5 D) μ = 8.9 24) n = 673; p =.7 24) A) μ = 472.8 B) μ = 469.6 C) μ = 472.4 D) μ = 471.1 Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 25) n = 49; p = 3/5 25) A) σ = 7.55 B) σ = 3.43 C) σ = 1.02 D) σ = 6.70 26) n = 1535; p =.57 26) A) σ = 19.40 B) σ = 16.99 C) σ = 22.67 D) σ = 23.52 Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ. 27) n = 100, p = 0.25 A) Minimum: 33.66; maximum: 16.34 B) Minimum: -12.5; maximum: 62.5 C) Minimum: 20.67; maximum: 29.33 D) Minimum: 16.34; maximum: 33.66 27) 28) n = 1042, p = 0.86 28) A) Minimum: 884.92; maximum: 907.32 B) Minimum: 880.28; maximum: 911.96 C) Minimum: 873.72; maximum: 918.52 D) Minimum: 918.52; maximum: 873.72 4
Solve the problem. 29) According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. 29) A) 4.00 B) 3.52 C) 2.75 D) 0.22 30) A die is rolled 7 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos. 30) A) 2.33 B) 1.17 C) 1.75 D) 5.83 31) The probability of winning a certain lottery is 1/78,651. For people who play 688 times, find the mean number of wins. 31) A) 0.000013 B) 0.0087 C) 114.3 D) 0.0015 32) According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16. 32) A) 1.88 B) 3.52 C) 2.75 D) 1.66 33) A company manufactures batteries in batches of 13 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch. 33) A) 0.624 B) 0.613 C) 0.591 D) 0.615 Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ. 34) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 638 consumers who recognize the Dull Computer Company name? 34) A) No B) Yes 35) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 553 consumers who recognize the Dull Computer Company name? 35) A) No B) Yes 5
Answer Key Testname: CH 5 SET 1 1) B 2) B 3) Not a probability distribution. The sum of the P(x)ʹs is not 1. 4) Probability distribution 5) B 6) A 7) C 8) D 9) C 10) B 11) A 12) D 13) B 14) A 15) A 16) B 17) C 18) A 19) C 20) D 21) A 22) B 23) A 24) D 25) B 26) A 27) D 28) C 29) B 30) B 31) B 32) D 33) D 34) B 35) A 6