Exam 4: Displaying and Comparing Qualitative Data

A new clothing store advertises that during its Grand Opening every customer that enters the store can throw a bouncy rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions award a 10% discount, two regions award a 20% discount, two regions award a 30% discount, and the remaining region awards a 50% discount. Show your work. 10 30 10 30 10 20 10 50 10 20 -What is the probability that none of the first three customers gets more than a 30% discount?

BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How many batteries would you expect to buy, on average, to find one that does not work?

On a physical fitness test middle school boys are awarded one point for each push-up they can do, and a point for each sit-up. National results showed that boys average 18 pushups with a standard deviation of 4 push-ups, and 34 sit-ups with standard deviation 11. The mean of their combined (total) scores was therefore 18 + 34 = 52 points. What is the standard deviation of their combined scores?

Verify that this scenario satisfies all four conditions for a binomial scenario.

A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat ham, and 16% have both turkey and ham to eat at holiday meals. a. What is the probability that a family selected at random had neither turkey nor ham at their holiday meal? b. What is the probability that a family selected at random had only ham without having turkey at their holiday meal? c. What is the probability that a randomly selected family having turkey had ham at their holiday meal? d. Are having turkey and having ham disjoint events? Explain.

According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computer in 2001. What is the probability that of three randomly selected U.S. households at least one owned a computer in 2001?

In an AP* Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. -What is the probability that a student from this class eats breakfast but does not floss their teeth?

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs. -What are the mean and standard deviation of the company's annual expense for the service contract?

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. -Surprised by the high number of customers who purchased specialty pet clothing that day, the owner decided that her 4% estimate must have been too low. How many clothing sales would it have taken to convince you? Justify your answer.

At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents on the boat on at least one visible feature. And 60% have both features. -What is the probability that if a boat has chrome accents it is also made of natural wood?

Political analysts estimate the probability that Hillary Clinton will run for president in 2008 is 45%, and the probability that NY's Governor George Pataki will run as the Republican candidate is 20%. If their political decisions are independent, then what is the probability that only Hillary runs for president?

An ice cream stand reports that 12% of the cones they sell are "jumbo" size. You want to see what a "jumbo" cone looks like, so you stand and watch the sales for a while. What is the probability that the first jumbo cone is the fourth cone you see them sell?

Some marathons allow two runners to "split" the marathon by each running a half marathon. Alice and Sharon plan to split a marathon. Alice's half-marathon times average 92 minutes with a Standard deviation of 4 minutes, and Sharon's half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women's half-marathon times are independent. The expected time for Alice and Sharon to complete a full marathon is 92 + 96 = 188 minutes. What is the standard deviation of their total time?

All airline passengers must pass through security screenings, but some are subjected to additional searches as well. Some travelers who carry laptops wonder if that makes them more likely to be searched. Data for 420 passengers aboard a cross-country flight are summarized in the table shown. Does it appear that being subjected to an additional search is independent of carrying a laptop computer? Explain. Searched? Yes No Total Laptop 30 42 72 No laptop 145 203 348 Total 175 245 420

If my dresser drawer has 10 blue socks and 12 black socks and I randomly pull out two socks, what are the chances that they are both black?

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more profitable. Before making a final decision he decides that for one day he'll keep track of the number of customers and whether or not they buy a magazine. -Assuming the owner is correct in thinking that 5% of the customers purchase magazines, how many customers should he expect before someone buys a magazine?

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of pulling out at least one green candy in three tries is...

If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances of rolling exactly three successes?

A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both features -What is the probability that a randomly selected bicycle will have a kickstand or a water bottle holder?

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. probability 0.10 0.25 0.55 0.10 \# of workers 3 4 5 6 If the workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?