Exam 4: Displaying and Comparing Qualitative Data

Cigarette taxes New York public health officials report that currently 22% of adults smoke (Ithaca Journal, 1/12/04). They hope that newly increased state cigarette taxes will reduce this rate. They plan to check in December by selecting a random sample of 1200 New Yorkers to estimate again the percentage of adults who smoke. a. Verify that a Normal model is a useful approximation for the binomial in this situation. b. In that December sample, how many smokers would it take to convince you that the percentage of NY adults who smoke had decreased significantly? Explain.

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. -The yearly service contract for the food fryer estimates a mean annual cost of $140 with a standard deviation of $40. What is the expected value and standard deviation of the total cost for the service contracts for the freezer and the food fryer?

Which of these random variables has a geometric model?

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. -If the monkeys enjoy this activity every night for an entire week, what are the chances that a monkey falls off the bed every one of the seven nights?

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 -As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Comment on their statements.

Jacob has a bag of his favorite marbles. It has 3 red marbles, 4 blue and 10 of his most favorite color, neon orange. -What are the chances that he as he removes marbles from the bag, he doesn't get an orange marble until his fourth attempt?

Bowling A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of 9 pins, while the women had mean score 144 pins and standard deviation 12 pins. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round. a. On average, how much do you expect the man to win by? b. Estimate the standard deviation of the differences in the competitor's scores. c. What assumption did you make in determining the standard deviation?

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. -He had 280 customers that day. Assuming this day was typical for his store, what would be the mean and standard deviation of the number of customers who buy magazines each day?

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 are the mean and standard deviation for the profit on a 1000 plans?

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

A young boy is fishing off the end of a dock. He estimates that for one out of every 15 times he casts his line, he gets at least a nibble from a curious fish. He is going to cast his line 50 times before he switches to toad hunting. -If he gets only 5 nibbles on his line, is that a signal that he is having less success than usual? Justify your answer.

A sporting goods store announces a “Wheel of Savings” sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free! Show your work. -What is the probability that there is at least one gold winner among the first six customers?

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. -We can tell that these two features are independent because...

Five multiple choice questions, each with four possible answers, appear on your history exam. What is the probability that if you just guess, you a. get none of the questions correct? b. get all of the questions correct? c. get at least one of the questions wrong? d. get your first incorrect answer on the fourth question?

Which of these random variables has a binomial model?

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. -Which service contract should the company expect to cost more each year? How much more? With what standard deviation?

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 exactly 3 of the first 10 customers buy specialty clothes for their pet? Show work.

A friend of yours plans to toss a fair coin 200 times. You watch the first 40 tosses, noticing that she got only 16 heads. But then you get bored and leave. If the coin is fair, how many heads do you expect her to have when she has finished the 200 tosses?

A biology professor responds to some student questions by e-mail. The probability model below describes the number of e-mails that the professor may receive from students during a day. E-mails received 0 1 2 3 4 5 Probability 0.05 0.10 0.20 0.25 0.30 0.10 a. How many e-mails should the professor expect to receive each day? b. What is the standard deviation? c. If it takes the professor an average of ten minutes to respond to each e-mail, how much time should the professor expect to spend responding to student e-mails each day?

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 or flosses their teeth?