Chapter 4 1) Golf Equipment Website Visitors. ParFore created a website to market golf equipment and golf apparel. Management would like a special pop-up offer to appear for female website visitors and a different special pop-up offer to appear for male website visitors. From a sample of past website visitors, ParFore's management learned that 60% of the visitors are male and 40% are female. a) What is the probability that a current visitor to the website is female? b) Suppose 30% of Pa rFore's female visitors previously visited the Dillard's department store website and 10% of ParFore's male visitors previously visited the Dillard's department store website. If the current visitor to ParFore's website previously visited the Dillard's website, what is the revised probability that the current visitor is female? Should the ParFore's website display the special offer that appeals to female visitors or the special offer that appeals to male visitors? 2) MBA New-Matriculants Survey. An MBA new-matriculants survey provided the following data for 2018 students. Applied thMore Than One School Yes No 23 and under 2426 \"'9\" 27-30 GNP 31-35 36 and ovar a) For a randomly selected MBA student, prepare a joint probability table for the experiment consisting of observing the student's age and whether the student applied to one or more schools. b) What is the probability that a randomly selected applicant is 23 or under? c) What is the probability that a randomly selected applicant is older than 26? d) What is the probability that a randomly selected applicant applied to more than one school? 3) MBA New-Matricula nts Survey. Refer again to the data from the MBA new matriculants survey in exercise 2). a) Given that a person applied to more than one school, what is the probability that the person is 2426 years old? b) Given that a person is in the 36-and-over age group, what is the probability that the person applied to more than one school? c) What is the probability that a person is 24-26 years old or applied to more than one school? d) Suppose a person is known to have applied to only one school. What is the probability that the person is 31 or more years old? e) Is the number of schools applied to independent ofage? Explain. 4) Students Studying Abroad. According to a report. 9.5% of undergraduate students in the U.S. study abroad as part of their education. Assume that 60% of the undergraduate students who study abroad are female and that 49% of the undergraduate students who do not study abroad are female. a) Given a female undergraduate student, what is the probability that she studies abroad? b) Given a male undergraduate student, what is the probability that he studies abroad? c) What is the overall percentage of full-time female undergraduate students? What is the overall percentage of full-time male undergraduate students? 5) Spam E-mail Filters. A study by Forbes indicated that the five most common words appearing in spam e-mails are shipping!, today!, here!, available, and ngertips! Many spam filters separate spam from ham (e-mail not considered to be spam) through application of Bayes' theorem. Suppose that for one e-mail account, 1 in every 10 messages is spam and the proportions of spam messages that have the ve most common words in spam e-mail are given below. Spam E-mail Filters. A study by Forbes indicated that the five most common words appearing in spam e-mails are shipping!, today!, here!, available, and fingertips! Many spam filters separate spam from ham (e-mail not considered to be spam) through application of Bayes' theorem. Suppose that for one e-mail account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam e-mail are given below. shipping! .051 today! .045 here! .034 available .014 fingertips! .014 Also suppose that the proportions of ham messages that have these words a shipping! .0015 today! 0022 here! 0022 available .0041 fingertips! .0011 ) If a message includes the word shipping!, what is the probability the message is spam? If a message includes the word shipping!, what is the probability the message is ham? Should messages that include the word shipping! be flagged as spam? b) If a message includes the word today!, what is the probability the message is spam? If a message includes the word here!, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why?c) If a message includes the word available, what is the probability the message is spam? If a message includes the word ngertipsl, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? d) What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively? Chapter 5 5) Contributing to Household Income. A study conducted by the Pew Research Center showed that 75% of 18- to 34-year-olds living with their parents say they contribute to household expenses (The Wall Street Journal). Suppose that a random sample of fifteen 18- to 34-year-olds living with their parents is selected and asked if they contribute to household expenses. a) Is the selection ofthe fifteen 18- to 34wyear-olds living with their parents a binomial experiment? Explain. b) If the sample shows that none of the fifteen 18- to 34-year-olds living with their parents contributes to household expenses, would you question the results of the Pew Research Study? Explain c) What is the probability that at least 10 of the fifteen 18- to 34-year-olds living with their parents contribute to household expenses? 7) Airport Passenger-Screening Facility. Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. a) Compute the probability of no arrivals in a one-minute period. b) Compute the probability that three or fewer passengers arrive in a one-minute period. c) Compute the probability of no arrivals in a \"IS-second period. cl) Compute the probability of at least one arrival in a \"IS-second period 8) Wait Times at Car Repair Garages. The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of the categories rated. The following table provides a summary of the wait-time ratings (1 = Slow/Delays; 10 = Quick/On Time) for 40 randomly selected garages located in the province of Quebec, Canada. Wait-Time Rating Number of Garages 6 2 2 3 3 2 5 A CO 5 Co 10 6 a) Develop a probability distribution for x = wait-time rating. b) Any garage that receives a wait-time rating of at least 9 is considered to provide outstanding service. If a consumer randomly selects one of the 40 garages for their next car service, what is the probability the garage selected will provide outstanding wait- time service? c) What is the expected value and variance for x? d) Suppose that seven of the 40 garages reviewed were new car dealerships. Of the seven new car dealerships, two were rated as providing outstanding wait-time service. Compare the likelihood of a new car dealership achieving an outstanding wait-time service rating as compared to other types of service providers.9) Creating a Diversified Investment Portfolio. The KnowleslArmitage (KA) group at Merrill Lynch advises clients on how to create a diversified investment portfolio. One of the investment alternatives they make available to clients is the All World Fund composed of global stocks with good dividend yields. One of their clients is interested in a portfolio consisting of investment in the All World Fund and a treasury bond fund. The expected percent return of an investment in the All World Fund is 7.80% with a standard deviation of 1 8.90%. The expected percent return of an investment in a treasury bond fund is 5.50% and the standard deviation is 4.60%. The covariance of an investment in the All World Fund with an investment in a treasury bond fund is -'| 2.4. a) Which of the funds would be considered the more risky? Why? b) If KA recommends that the client invest 75% in the All World Fund and 25% in the treasury bond fund, what is the expected percent return and standard deviation for such a portfolio? What would be the expected return and standard deviation, in dollars, for a client investing $10,000 in such a portfolio? c) If KA recommends that the client invest 25% in the All World Fund and 75% in the treasury bond fund, what is the expected return and standard deviation for such a portfolio? What would be the expected return and standard deviation, in dollars, for a client investing $10,000 in such a portfolio? d) Which of the portfolios in parts (b) and (c) would you recommend for an aggressive investor? Which would you recommend for a conservative investor? Why? 10) Giving up Technology. A Pew Research Center survey asked adults in the United States which technologies would be "very hard" to give up. The following responses were obtained: Internet 53%. smartphone 49%, e-mail 36%, and land-line phone 28% (USA Today website). a) If 20 adult Internet users are surveyed, what is the probability that 3 users will report that it would be very hard to give it up? D) If 20 adults who own a land-line phone are surveyed, what is the probability that 5 or fewer will report that it would be very hard to give it up? c) If 2,000 owners of smartphones were surveyed, what is the expected number that will report that it would be very hard to give it up? d) If 2,000 users of e-mail were surveyed, what the expected number that will report that it would be very hard to give it up? What is the variance and standard deviation? Chapter 6 11) Bringing Items to a Pawnshop. One indicator of the level of economic hardship in a community is the number of people who bring items to a pawnbroker. Assume the number of people bringing items to the pawnshop per day is normally distributed with a mean of 658. a) Suppose you learn that on 3% of the days, 610 or fewer people brought items to the pawnshop. What is the standard deviation of the number of people bringing items to the pawnshop per day? b) On any given day, what is the probability that between 600 and 700 people bring items to the pawnshop? c) How many people bring items to the pawnshop on the busiest 3% of days? 12) Filling Weights. A machine lls containers with a particular product. The standard deviation of lling weights is known from past data to be .6 ounce. If only 2% of the containers hold less than 18 ounces, what is the mean filling weight for the machine? That is, what must p equal? Assume the lling weights have a normal distribution