1. In response to consumer concern about cholesterol and saturated fat in baked goods, a large bakery on the East Coast has decided to reformulate the ingredients used in making a particular cake. It will bake the cake without using any egg yolks. To determine consumer reaction to this new product, the company randomly selects 12 people and asks them to rate the cake (on a particular taste appeal scale) both before and after the egg yolks are removed.

a. Construct side-by-side boxplot for the data by separating the cakes with and without egg yolks and interpret it.

b. Produce a stem-and leaf display for the difference between scores.

d. Set up a 99% confidence interval for the difference between scores

2. Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the data that are based on the education level of the persons and whether they are financially better off, the same or worse off than their parents.

a. What is the probability that a randomly selected person is better off or high school graduate?

b. What is the probability that a randomly selected person has a less than high school education given that s/he is worse off?

c. Are the events "same" and "high school" independent? Are they disjoint? Please justify your answer.

3. An island has three species of bird. Species 1 accounts for 45% of the birds, of which 10% have been tagged. Species 2 accounts for 38% of the birds, of which 15% have been tagged. Species 3 accounts for 17% of the birds, of which 50% have been tagged.

a. What is the probability that a randomly selected bird will be tagged?

b. If a tagged bird is observed, what is the probability that it is of species 2?

4. The weights of bags filled by a machine are normally distributed with a standard deviation of 0.05 kg and a mean which can be set by the operator.

a. At what level should the mean be set if it is required that only 1% of the bags weigh less than 10kg?

b. Suppose that the mean is set to 10.02 kg. What is the probability that the average weight of 9 bags filled by this machine will be less than 10kg?

5. The number bone fracture patients entering to a hospital emergency room in one day has a Poisson distribution with mean 6.8 patients. The hospital manager has decided to allocate emergency room resources that are sufficient to comfortably cope with up to ten bone fracture patients per day. What is the probability that on a given day these resources will be inadequate.

a. The captain’s contractor have offered him a sizable bonus if s/he is able to reduce searching cost by locating the wreck within the first week. What is the probability that the captain will get the bonus?

b. The captain is only authorized to search for at most 4 weeks before calling off the search. What is the probability that the search will be called off?

c. The captain gets 10 such contracts. For each of them, the captain is only authorized to search for at most 4 weeks before calling off the search. What is the probability that at least half of these searches will be called off?

7. A zoologist is interested in determining the average life span of a certain species of elephant bred in captivity. The zoologist collects data on 15 elephants of this type from 15 different randomly selected zoos throughout America. The average life spans of these elephants is found to be 29.9 years with a standard deviation of 7.4 years.

a. Construct a 90% confidence interval for the true average life span of an elephant from this species.

8. (Source: "Demons Begone", Asheville Citizen-Times, April 5, 1991) A poll of 1,226 adults revealed that 601 of them believe that the devil may sometimes possess earthlings.

a. Construct a 90% confidence interval for the true proportion of adults who believe that the devil may sometimes possess earthlings.

b. Determine the sample size required the estimate will be within 0.02 of the true proportion with 90% confidence.

9. An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 68 miles per hour with a standard deviation of 2.2 miles. Another sample of 18 cars driven by women on the same highway gave a mean speed of 65 miles per hour with a standard deviation of 2.5 miles. Assume that the speeds at which all men and all women drive cars on this highway are both normally distributed.

a. Construct a 99% confidence interval for the difference between the mean speeds of cars driven by all men and all women drivers on this highway.

10. According to the National Household Survey on Drug Abuse, 8.2% of the 12- to 17-years-olds interviewed admitted to illicit drug use during the month before the survey in 1994, and the corresponding percentage was 10.9% for 1995 (USA Today, August 21, 1996). Assume that these estimates are based on random samples of 1800 and 2000 such young persons for 1994 and 1995, respectively.

a. Determine a 99% confidence interval for the difference between the population proportions of 12- to 17-year-olds who used illicit drugs in 1994 and 1995.