3 You have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together in 1%. What percent of these operations succeed and are free from infection?

4 An automobile manufacturer buys computer chips from a supplier. The supplier sends a shipment containing 5% defective chips. Each chip chosen from this shipment has probability 0.05 of being defective, and each automobile uses 12 chips selected independently. What is the probability that all 12 chips in a car will work properly?

5 In an experiment on the behavior of young children, each subject is placed in an area with five toys. The response of interest is the number of toys that the child plays with. Past experiments with many subjects have shown that the probability distribution of the number X of toys played with is as follows: xi 0 1 2 3 4 5 pi 0.03 0.16 0.3 0.23 0.17 0.11 Calculate the mean and the standard deviation.

6 Consolidated Builders has bid on two large construction projects. The company president believes that the probability of winning the first contract (event A) is 0.6, that the probability of winning the second (event B) is 0.5, and that the probability of winning both jobs (event {A and B}) is 0.3. What is the probability of the event {A or B} that Consolidated will win at least one of the jobs?

7 In the setting of the previous exercise, are events A and B independent? Justify your answer using probability

8 A university that is better known for its basketball program than for its academic strength claims that 80% of its basketball players get degrees. An investigation examines the fate of all 20 players who entered the program over a period of several years that ended 6 years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the university's claim is true, the number of players who graduate among the 20 studied should have the B(20; 0:8) distribution. (a) Find the probability that exactly 11 of the 20 players graduate. (b) Find the probability that 11 or fewer players graduate. This probability is so small that it casts doubt on the university's claim.

9 A factory employs several thousand workers, of whom 30% are Hispanic. If the 15 members of the union executive committee were chosen from the workers at random, the number of Hispanics on the committee would have the binomial distribution with n = 15 and p = 0:3. (a) What is the probability that exactly 3 members of the committee are Hispanic? (b) What is the probability that 3 or fewer members of the committee are Hispanic?

11 The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not normal. (a) Let x-bar be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of x-bar according to the central limit theorem? (b) What is the approximate probability that x-bar is less than 2? (c) What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of x.)

12 Leona and Fred are friendly competitors in high school. Both are about to take the ACT college entrance examination. They agree that if one of them scores 5 or more points better than the other, the loser will buy the winner a pizza. Suppose that in fact Fred and Leona have equal ability, so that each score varies normally with mean 24 and standard deviation 2. (The variation is due to luck in guessing and the accident of the specific questions being familiar to the student.) The two scores are independent. What is the probability that the scores differ by 5 or more points in either direction?

13 A student reads that a 95% confidence interval for the mean SAT math score of California high school seniors is 452 to 470. Asked to explain the meaning of this interval, the student says, “95% of California high school seniors have SAT math scores between 452 and 470." Is the student right? Justify your answer.

14 A test for the level of potassium in the blood is not perfectly precise. Moreover, the actual level of potassium in a person's blood varies slightly from day to day. Suppose that repeated measurements for the same person on different days vary normally with s = 0.2. (a) Julie's potassium level is measured once. The result is x = 3.4. Give a 90% confidence interval for her mean potassium level. (b) If three measurements were taken on different days and the mean result is x = 3.4, what is a 90% confidence interval for Julie's mean blood potassium level?

4.37 You have two balanced, six-sided dice. The first has 1, 3, 4, 5, 6, and 8 spots on its six faces. The second die has 1, 2, 2, 3, 3, and 4 spots on its faces. (a) What is the mean number of spots on the up-face when you roll each of these dice? (b) Write the probability model for the outcomes when you roll both dice independently. From this, find the probability distribution of the sum of the spots on the up-faces of the two dice. (c) Find the mean number of spots on the two up faces in two ways: from the distribution you found in (b) and by applying the addition rule to your results in (a).You should of course get the same answer.

4.38 You have two scales for measuring weights in a chemistry lab. Both scales give answers that vary a bit in repeated weighings of the same item. If the true weight of a compound is 2 grams (g), the first scale produces readings X that have mean 2.000 g and standard deviation 0.002 g. The second scale's readings Y have mean 2.001 g and standard deviation 0.001 g. (a) What are the mean and standard deviation of the difference Y −X between the readings? (The readings X and Y are independent.) (b) You measure once with each scale and average the readings. Your result is Z = (X + Y )=2. What are the mean and standard deviation of Z? Is the average Z more or less variable than the reading Y of the less variable scale? [Hint: rewrite Z]