Problem 33
A newly hired telemarketer is told he will probably make a sale on about \(12 \%\) of his phone calls. The first week he called 200 people, but only made 10 sales. Should he suspect he was misled about the true success rate? Explain.
Problem 34
Shortly after the introduction of the euro coin in Belgium, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads - that's \(56 \%\) heads. Do you think this is evidence that spinning a euro is unfair? Explain.
Problem 35
Police estimate that \(80 \%\) of drivers now wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. a) How many cars do they expect to stop before finding a driver whose seatbelt is not buckled? b) What's the probability that the first unbelted driver is in the 6 th car stopped? c) What's the probability that the first 10 drivers are all wearing their seatbelts? d) If they stop 30 cars during the first hour, find the mean and standard deviation of the number of drivers expected to be wearing seatbelts. e) If they stop 120 cars during this safety check, what's the probability they find at least 20 drivers not wearing their seatbelts?
Problem 36
Vitamin D is essential for strong, healthy bones. Our bodies produce vitamin D naturally when sunlight falls upon the skin, or it can be taken as a dietary supplement. Although the bone disease rickets was largely eliminated in England during the 1950 s, some people there are concerned that this generation of children is at increased risk because they are more likely to watch TV or play computer games than spend time outdoors. Recent research indicated that about \(20 \%\) of British children are deficient in vitamin D. Suppose doctors test a group of elementary school children. a) What's the probability that the first vitamin Ddeficient child is the 8 th one tested? b) What's the probability that the first 10 children tested are all okay? c) How many kids do they expect to test before finding one who has this vitamin deficiency? d) They will test 50 students at the third-grade level. Find the mean and standard deviation of the number who may be deficient in vitamin D. e) If they test 320 children at this school, what's the probability that no more than 50 of them have the vitamin deficiency?
Problem 38
A true-false test consists of 50 questions. How many does a student have to get right to convince you that he is not merely guessing? Explain.
Problem 39
A basketball player who ordinarily makes about \(55 \%\) of his free throw shots has made 4 in a row. Is this evidence that he has a "hot hand" tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Explain.
Problem 41
Our basketball player in Exercise 39 has new sneakers, which he thinks improve his game. Over his past 40 shots, he's made 32 -much better than the \(55 \%\) he usually shoots. Do you think his chances of making a shot really increased? In other words, is making at least 32 of 40 shots really unusual for him? (Do you think it's his sneakers?)
