Fillable Problems Probability Models Worksheets (Page 4 of 11) in pdf

25. Lefties again. A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The

average size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. What's

the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet?

26. No-shows. An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than

there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What's the probability the

airline will not have enough seats so someone gets bumped?

27. Annoying phone calls. 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.

28. The euro. 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.

29. Seatbelts II. 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 6th 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?

30. Rickets. 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 1950s, 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 D-deficient child is the 8th 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?

31. ESP. Scientists wish to test the mind-reading ability of a person who claims to "have ESP." They use five cards with

different and distinctive symbols (square, circle, triangle, line, squiggle). Someone picks a card at random and thinks

about the symbol. The "mind reader" must correctly identify which symbol was on the card. If the test consists of 100

trials, how many would this person need to get right in order to convince you that ESP may actually exist? Explain.

32. True-False. 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.

33. Hot hand. 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.

34. New bow. Our archer in Exercise 14 purchases a new bow, hoping that it will improve her success rate to more than

80% bull's-eyes. She is delighted when she first tests her new bow and hits 6 consecutive bull's-eyes. Do you think

this is compelling evidence that the new bow

Problems Probability Models Worksheets Page 4

Related Articles

Related forms

Related Categories