And the rest of the people were from River City. Out of the sample, 19 people had some form of cancer. Thirteen of these people were from Laketown. (a) Are the events of living in Laketown and having some sort of cancer independent? (b) Which city would you prefer to live in, assuming that your main objective was to avoid having cancer? : 2-28 Compute the probability of "loaded die, given that a 3 was rolled," as shown in Example 7, this time using the general form of Bayes' theorem from Equation 2-7. • 2-29 Which of the following are probability distributions? Why? (a)
LOOM VARIABLE
• 2-31 What are the expected value and variance of the fol-lowing probability distribution?
-2 -1 0 1 2 0.1 0.2 0.3 0.25 0.15 X (b) 1 1.1 1.5 0.2 0.3 X 2.5 0.25 3 -1.25 (c) X: 444'2 1 0.1 2 0.2 3 0.3 4 0.4 5 0.0
• 2-30 Harrington Health Food stocks 5 loaves of Neutro-Bread. The probability distribution for the sales of Neutro-Bread is listed in the following table. How many loaves will Harrington sell on average?
UMBER OF I AVE8 4 0 0.05 1 0.15 2 0.20 3 0.25 4 0.20 5 0.15
. 5 Amain' 0.05 0.05 3 0.10 4 0.10 5 0.15 6 0.15 7 0.25 8 0.15
2-32 There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7 correct? (b) What is the probability that the student gets exactly 8 correct? (c) What is the probability that the student gets exactly 9 correct? (d) What is the probability that the student gets exactly 10 correct? (e) What is the probability that the student gets more than 6 correct? 2-33 Gary Schwartz is the top salesman for his company. Records indicate that he makes a sale on 70% of his sales calls. If he calls on four potential clients, what is the probability that he makes exactly 3 sales? What is the probability that he makes exactly 4 sales? 2-34 If 10% of all disk drives produced on an assembly line are defective, what is the probability that there will be exactly one defect in a random sample of 5 of these? What is the probability that there will be no defects in a andom sample of 5? Trowbridge Manufacturing produces cases for personal
computers and other electronic equipment. The quality control inspector for this company believes that a par-ticular process is out of control. Normally, only 5% of all cases are deemed defective due to discolorations. If 6 such cases are sampled, what is the probability that there will be 0 defective cases if the process is operating correctly? What is the probability that there will be exactly 1 defective case? 2-36 Refer to the Trowbridge Manufacturing example in Problem 2-35. The quality control inspection proce-dure is to select 6 items, and if there are 0 or 1 defec-tive cases in the group of 6, the process is said to be in control. If the number of defects is more than 1, the process is out of control. Suppose that the true pro-portion of defective items is 0.15. What is the proba-bility that there will be 0 or 1 defects in a sample of 6 if the true proportion of defects is 0.15? 2-37 An industrial oven used to cure sand cores for a fac-tory manufacturing engine blocks for small cars is
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