Exercises for Chapter (5)

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1 Exercises for Chapter (5) MULTILE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 500 families were interviewed and the number of children per family was determined. The data were summarized as follows: Number of children per family (x) Number of families If you randomly select a family from the 500 families interviewed, what is the probability that the selected family has 3 children? A) 0.06 ) 50 C) 0.50 D) ) The random variable X has the following distribution: X (x) ? Find (X = 10) A) 0.3 ) 0.2 C) 0.5 D) 0.1 3) The random variable X has the following distribution: X (x) ? The mean and standard deviation of X are, respectively, A) 0, 3.0 ) 4.5, 3.75 C) 4.5, D) 1.5, ) The random variable X has the following distribution: X (x) ? Find the probability that X exceeds 2. A) 0.5 ) 0.6 C) 0.7 D) 0.2 5) An analyst estimates that a stock has the following probabilities of return depending on the state of the economy. Economy Return robability Good 15% 0.1 Normal 13% 0.6 oor 7% 0.3 1) 2) 3) 4) 5) The expected return of the stock is: A) 11.7% ) 7.8% C) 11.4% D) 13.0% 6) The following table summarizes investment outcomes (in $1000) and corresponding probabilities for a particular oil well: x = the outcomes (in $1000) (x) - 4 (no oil) Total 1 6) Find the expected value of the investment outcomes A) 1.0 ) 2.0 C) 0.05 D)

2 7) The following table summarizes investment outcomes (in $1000) and corresponding probabilities for a particular oil well: x = the outcomes (in $1000) (x) - 4 (no oil) Total 1 7) Find the standard deviation for the investment outcomes A) 2.67 ) 6.72 C) 7.15 D) ) Abdullah is considering an investment in a company. He is interested in buying a number of shares of this company and keep them for one year. The price of a single share at this time is $16 and the forecasted price a year from today is given in the following table 8) rice of stock in one year robability Does the information above describe a valid probability distribution function? A) None of the above ) No, since x 1 C) yes D) No, since p(x) 1 9) Abdullah is considering an investment in a company. He is interested in buying a number of shares of this company and keep them for one year. The price of a single share at this time is $16 and the forecasted price a year from today is given in the following table 9) rice of stock in one year robability What is the variance and standard deviation of the stock price a year from today? A) 1.725, ) 2.765, C) 17.07, D) 1.117, ). The number of connections on the internet during two-minute period is given by the following distribution Number of times roportion Determine the mean number of times a connection is made during a two-minute period A) 2.2 ) 2.7 C) 2.5 D) ). The number of connections on the internet during two-minute period is given by the following distribution Number of times roportion Determine the standard deviation of the number of times a connection is made during a two-minute period A) 1.88 ) 1.64 C) 2.28 D) ) 11) 2

3 12) A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make profit of $5,000 with probability 9/20, to break even (i.e. profit = 0) with probability 1/4 and to lose $5,000 with probability 3/20. The expected profit in dollars is: i.e. 12) A) $1500 ) $-1500 C) $3250 D) $ ) Suppose 60% of a large group of animals is infected with a particular disease. Let Y= the number of non- infected animals in a sample of size 5. The distribution of Y is A) binomial with n = 5 and p = 0.4 ) binomial with n = 5 and p = 0.5 C) oisson with = 0.60 D) binomial with n = 5 and p = ) 14) Whenever p = 0.9 and n = 10, the mean of the binomial random variable will be 14) A) 0.9 ) 9 C) 0.95 D) 10 H 15) A class consists of 45 students. Ten of these students received an "A" for the final exam. Five students are selected at random from this group. Using the Hyper-geometric distribution what is the probability that at least one of the five students selected received an "A" for the final exam? A) ) C) D) ) 16) The number of traffic accidents in a small city has a rate (average) of 3 accidents per week. What is the probability of at least one accident in 2 weeks? A) ) C) D) ) 17) The number of telephone calls that pass through a switchboard has a oisson distribution with mean equal to 2 per minute. The expected number of phone calls that pass through the switchboard in one minute is A) 2 ) 1 C) 4 D) 3 17) H 18) The number of telephone calls that pass through a switchboard has a oisson distribution with mean equal to 2 per minute. The probability that no telephone calls pass through the switchboard in two consecutive minutes is A) ) C) D) ) A company has bought 20 machines from a manufacturer. The manufacturer advises them that 8 of these machines have a defect. They take a random sample of 5 machines. What is the probability that exactly 2 of the machines in the sample have a defect? A) ) C) D) ) 19) 20) Which of the following is not true concerning discrete probability distribution? 20) A) The standard deviation of the distribution is between -1 and 1. ) The sum of all probabilities is 1. C) The mean of the distribution is between the smallest and largest value of the discrete random variable. D) The probability of any specific value is between 0 and 1, inclusive. E) The distribution may be displayed using a probability histogram. 21) The discrete probability distribution that may be used to compute the probability of occurrence of a random event over some particular time period would be the distribution A) oisson ) binomial C) hypergeometric D) none of these 21) 3

4 H 22) When sampling without replacement from a finite population, the data follow 22) A) a hypergeometric distribution ) a oisson distribution C) a normal distribution D) a binomial distribution 23) A multiple choice test has 20 questions, with each question having 5 possible answers. Suppose a student randomly guesses the answer of each question. What is the probability that the student will answer all 20 questions correctly? A) 0.20 ) 0.05 C) D) ) 24) For a binomial distribution 24) A) There must be at least 3 possible outcomes ) must be multiple of 0.10 C) n must assume a number between 1 and 20. D) None of the above 25) A new treatment is developed. It is said that the probability of a randomly selected patient being cured by this treatment is If 5 patients receive this treatment, what is the probability that at least 4 of them will be cured? A) ) C) D) ) 26) The number of traffic accidents per day on a certain section of highway is assumed to be oisson with a mean equal to 4. ased on this, how many traffic accidents should be expected during any give week? A) 28 ) 16 C) 20 D) 4 26) 27) In a certain communication system, there is an average of 1 transmission error per 10 seconds. Let the distribution of transmission errors be oisson. What is the probability of having 2 errors in one-half minute in duration A) ) C) D) ) 28) The number of customers entering a bank per minute is a oisson random variable with a mean of 3.5 customers per minute. What is the probability that more than three customers enter the bank in a minute? A) ) C) D) ) 29) The marketing manager of a company usually receives 10 complaint calls during a week (consisting of five working days). Suppose that the number of calls during a week follows the oisson distribution. The probability that she gets five such calls in one day is: A) ) C) D) ) 30) The probability that a certain machine will produce a defective item is If a random sample of 6 items is taken, what is the probability that there will be 5 or more defectives in the sample? A) ) C) D) ) H 31) The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MA students should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two? A) ) C) D) ) 4

5 H 32) Suppose a professor randomly selects three new teaching assistants from a total of 10 applicants, six male and four female students. The probability that no females are hired is A) ) C) D) ) 33) A large proportion of small businesses fail during the first few years of operation. On average, 1.3 businesses fail per day in a large city. What is the probability that 3 businesses will fail on a given day in this city? A) ) C) D) ) 34) The distribution of the number of people logging into a large computer network during a five second period is A) oisson ) Hypergeometric C) None of the above D) binomial 34) 35) According to a survey, 75% of all customers will return to the same grocery store. Suppose eight customers are selected at random, what is the probability that exactly five of the customers will return? A).2541 ) C) D) ) 36) According to a survey, 75% of all customers will return to the same grocery store. Suppose eight customers are selected at random. How many customers would be expected to return to the same store? A) 6 ) 5 C) 7 D) 8 36) 37) 29. Which of the following is NOT an assumption of the binomial experiment? 37) A) All trials must be identical and independent ) The number of successes in the trials is counted. C) Each trial outcomes must be classified as a success or a failure. D) The probability of success is equal to 0.5 in all trials 38) A retail store aimed to reduce the number of bad checks cashed by its cashiers. The average number of bad checks cashed is three per week. Let x denote the number of bad checks cashed per week. Assuming that x has a oisson distribution. Find the probability that the store's cashiers will not cash any bad checks in a particular week. A).0498 ).1494 C).0550 D) ) 39) A retail store aimed to reduce the number of bad checks cashed by its cashiers. The average number of bad checks cashed is three per week. Let x denote the number of bad checks cashed per week. Assuming that x has a oisson distribution. Find the probability that the store's cashiers will cash no more than 4 bad checks per two-week period. A).1512 ).7149 C).2851 D) ) 40) A retail store aimed to reduce the number of bad checks cashed by its cashiers. The average number of bad checks cashed is three per week. Let x denote the number of bad checks cashed per week. Assuming that x has a oisson distribution. Find the mean, variance, and standard deviation of the number of bad checks per week? A) 3, 1.73, 3 ) 3, 3, 3.17 C) 3, 3, 1.73 D) 1.73, 3, 5 40) 5

6 41) A committee of three people is to be selected from a group of five men and three women. Find the probability that at least two men are on the committee. A).1786 ).3471 C).9821 D) ) In a market study, a researcher found that 70% of customers are repeat customers. If 10 customers are selected at random, find the probability that at least three customer is repeat customer. A).9986 ) C) D) ) In a market study, a researcher found that 70% of customers are repeat customers. If 10 customers are selected at random, find the probability that exactly 7 are repeat customers. A).2503 ).2668 C).2001 D) ) In a market study, a researcher found that 70% of customers are repeat customers. If 10 customers are selected at random, find the probability that. How many would you expect to be repeat customers? A) 70 ) 6 C) 7 D) 10 45) A retailer of electronic equipment received nine cassettes from the manufacturer. Three of the cassettes were damaged in the shipment. The retailer sold three cassettes to three customers. Let X denotes the number of damaged cassettes sold to the three customers. a. Write the probability function of X. 41) 42) 43) 44) 45) A) (x)= C 6 x C 6 3-x C 9 3 ) (x)= C 6 x C 3 3-x C 9 3 C) (x)= C 3 x C 6 3-x C 6 3 D) (x)= C 3 x C 6 3-x C ) A retailer of electronic equipment received nine cassettes from the manufacturer. Three of the cassettes were damaged in the shipment. The retailer sold three cassettes to three customers. Let X denotes the number of damaged cassettes sold to the three customers. What is the probability that two of the three customers received damaged cassettes? A) ) C) D) ) A retailer of electronic equipment received nine cassettes from the manufacturer. Three of the cassettes were damaged in the shipment. The retailer sold three cassettes to three customers. Let X denotes the number of damaged cassettes sold to the three customers. What is the probability that not more than one of the three customers received damaged cassettes? A) ) C) D) ) In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that 4 females are selected? A) ) C) D) ) 47) 48) 6

7 49) In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that at most one male is selected? A) ) C) D) ). Customers use an automatic teller machine at an average of 5 per hour. What is the probability that exactly 12 will use the machine in the next hour? A) ) C) D) ). Customers use an automatic teller machine at an average of 15 per hour. What is the probability that at least one will use the machine in the next 20 minutes? A).0337 ).9339 C).9933 D) ) A bag contains 7 English books and 5 Math books. Suppose that you randomly select 4 books from the bag. Let X be the number of Math books in these 4 books that will be selected from the bag. Write the probability distribution of X? 49) 50) 51) 52) A) (x)= C) (x)= C 5 x C 7 4-x C 12 4 C 12 x C 7 4-x C 12 4 ) (x)= D) (x)= C 7 x C 5 4-x C 12 4 C 5 12 x C 4-x C ) A bag contains 7 English books and 5 Math books. Suppose that you randomly select 4 books from the bag. Let X be the number of Math books in these 4 books that will be selected from the bag. What is the probability that you select two Math and two English books? A).5758 ).8774 C).4588 D) ) An auto assembly worker requires 4 electrical fuses for each vehicle. The supplier of the fuses has informed the plant manager that 5% of all the fuses they produce are defective. Assume that the assembly worker selects the 4 fuses for any vehicle at random and independently of each other A) ) C) D) ) We believe that 80% of the population of all usiness Statistics I students consider statistics to be an exciting subject. Suppose we randomly and independently selected 15 students from the population. Find the probability of observing 13 or more students who consider statistics to be an exciting subject. A) ) C) D) E) ) A recent survey found that 72% of all adults over 50 wear glasses for driving. In a random sample of 100 adults over 50, what is the mean and standard deviation of the number who wear glasses? A) mean: 28; standard deviation: 4.49 ) mean: 28; standard deviation: 8.49 C) mean: 72; standard deviation: D) mean: 72; standard deviation: 8.49 E) mean: 72; standard deviation: ) 54) 55) 56) 7

8 57) As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability that one of the two phones is faulty. A).0775 ).4615 C).5380 D).2310 E) ) Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions. A).4330 ).1600 C).3600 D).3429 E) ) Suppose the number of babies born each hour at a hospital follows a oisson distribution with a mean of 5. Find the probability that exactly four babies will be born during a particular 1-hour period at this hospital. A) ) C) D) E) ) A small life insurance company has determined that on the average it receives 6 death claims per day. Find the probability that the company receives at most 2 death claims on a randomly selected day. A) ) C) D) E) ) The number of calls, X, that come to an office can be modeled by a oisson model with a mean rate of = 6 calls per hours.what is the probability that the office receives at least one call in any given one-hour time interval? A).9973 ).9970 C).0003 D).3354 E) ) The number of calls, X, that come to an office can be modeled by a oisson model with a mean rate of = 8 calls per hours.. A trainee has to take over for the office for 30 minutes (one-half hour). What is the probability that at least 2 calls come in during this time period? A).8535 ).4985 C).7619 D).1465 E) ) 58) 59) 60) 61) 62) 8

9 Answer Key Testname: QM120_EXERCISES FOR CHATER 5 1) D 2) A 3) 4) A 5) C 6) C 7) A 8) C 9) A 10) D 11) D 12) D 13) A 14) 15) A 16) A 17) A 18) C 19) 20) A 21) A 22) A 23) D 24) D 25) A 26) A 27) D 28) C 29) C 30) C 31) A 32) 33) A 34) A 35) C 36) A 37) D 38) A 39) C 40) C 41) D 42) A 43) 44) C 45) D 46) A 47) C 48) D 49) D 50) C 9

10 Answer Key Testname: QM120_EXERCISES FOR CHATER 5 51) C 52) A 53) D 54) A 55) C 56) E 57) 58) D 59) D 60) 61) E 62) E 10

STT 315 Practice Problems Chapter 3.7 and 4

STT 315 Practice Problems Chapter 3.7 and 4 Answer the question True or False. 1) The number of children in a family can be modelled using a continuous random variable. 2) For any continuous probability