Exam 4: Displaying and Comparing Qualitative Data

A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs. -How many times should the restaurant expect to have to get this freezer repaired over the three-year term of the lease?

A national study found that the average family spent $422 a month on groceries, with a standard deviation of $84. The average amount spent on housing (rent or mortgage) was $1120 a month, With standard deviation $212. The expected total a family spends on food and housing is 422 + 1120= $1542. What is the standard deviation of the total?

Which of these has a geometric model?

The Masterfoods company manufactures bags of Peanut Butter M&M's. They report that they make 10% each brown and red candies, and 20% each yellow, blue, and orange candies. The rest of the candies are green. a. If you pick a Peanut Butter M&M at random, what is the probability that i. it is green? ii. it is a primary color (red, yellow, or blue)? iii. it is not orange? b. If you pick four M&M's in a row, what is the probability that i. they are all blue? ii. none are green? iii. at least one is red? iv. the fourth one is the first one that is brown? c. After picking 10 M&M's in a row, you still have not picked a red one. A friend says that you should have a better chance of getting a red candy on your next pick since you have yet to see one. Comment on your friend's statement.

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. -Given that a randomly selected bike has a kickstand, what are the chances that it also has a water bottle holder?

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. -How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood?

Which of these random variables is most likely to have a binomial model?

Carpet A store selling carpet tracks the amount of square footage sold to its customers, rounding to the nearest 500 sq. ft. Here is the distribution. area 500 sq. ft. 1000 sq. ft. 1500 sq. ft. 2000+ sq. ft. probability 0.10 0.25 0.45 0.20 a. What is the average expected area sold? b. If the average cost of carpet sold is $3/sq. ft., what is the average sale price per customer? c. If a salesman completes sales to five customers one day, what do you expect his total sales to be?

Which of these has a Geometric model?

A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of customers will need the replacement voucher and 10% will request a repair. -What is the standard deviation of their profit?

A survey of some AP* Stats students recorded gender and whether the student was left or right-handed. Results were summarized in a table like the one shown. If it turned out that handedness was independent of gender, how many of the AP* Stats students were lefty girls? Lefty Righty Total Boy 66 Girl ? 54 Total 20 100 120

A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. Results are as follows: $\quad\quad\quad\quad\quad\quad\quad\quad\text { Breakfast }$ start text Sex end text Yes No Total Male 66 66 132 Female 125 74 199 Total 191 140 331 a. What is the probability that a randomly selected student is female? b. What is the probability that a randomly selected student ate breakfast? c. What is the probability that a randomly selected student is a female who ate breakfast d. What is the probability that a randomly selected student is female, given that the student ate breakfast? e. What is the probability that a randomly selected student ate breakfast, given that the student is female? f. Does it appear that whether or not a student ate breakfast is independent of the student's sex? Explain.

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed. -The monkeys manage to go a whole week without someone bumping their head. One of the kangaroos insists that they are due for an injury. Another says they must be getting better at their jumping skills. Do you think they're due for a crash?

A supermarket claims that their checkout scanners correctly price 99.8% of the items sold. How many items would you expect to buy, on average, to find one that scans incorrectly?

Which of these has a Binomial model?

The American Veterinary Association claims that the annual cost of medical care for dogs averages $100 with a standard deviation of $30, and for cats averages $120 with a standard deviation of$35. a. Find the expected value for the annual cost of medical care for a person who has one dog and one cat. b. Find the standard deviation for the annual cost of medical care for a person who has one dog and one cat. c. Suppose that a couple owns four dogs. i. Find the expected value for the annual cost of medical care for the couple's dogs. ii. Find the standard deviation for the annual cost of medical care for the couple's dogs.

A poll of 120 Ithacans found that 30 had visited the Museum of the Earth, and that 80 had been to Home Depot. If it appeared that going to Home Depot and going to the Museum of the Earth were independent events, how many of those polled had been to both? Museum Yes No Total Home Yes ?? 80 Depot No 40 Total 30 90 120

SAT prep Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students. You overhear a classmate say he got into the college he wanted. What is the probability he didn't take an SAT prep course?

A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished all 200 tosses?

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. -What is the probability that at least 5 of his first 50 customers buy magazines?