The NCAA Men’s and Women’s Swimming and Diving Committee recently recommended a no recall false-start rule.35 This proposal means that unless a false start is blatant, the race will continue. The student-athlete committing the false start will be disqualified following the event. Suppose the probability of a false start in any swimming event is 0.07, and swimming events are selected at random.
a. What is the probability that the first false start will occur in the fourth event selected?
b. What is the probability that the first false start will occur after the 15th event selected?
c. What is the mean number of events selected before a false start occurs?
d. Suppose there are 26 events at a swimming and diving meet. What is the probability that the first false start will occur at this meet?
Flatpanel TV displays in televisions and computer monitors often develop dead pixels, pixels that become locked in one state—for example, red at all times. Manufacturers maintain that dead pixels are a natural defect and there are various return policies after the discovery of a dead pixel. Suppose the mean number of dead pixels in a new Samsung 64-inch plasma TV is 2.5. One of these TVs is randomly selected and inspected for dead pixels.
a. What is the probability that there will be no dead pixels?
b. If the number of dead pixels is more than
the assembly line is automatically stopped and examined. What is the probability that the assembly line will be stopped?
c. What is the probability that the number of dead pixels will be within two standard deviations of the mean?
Most banks charge a monthly fee for a checking account, in addition to ATM, overdraft, and other fees. However, 72% of credit unions offer checking accounts with no monthly fees.36 Suppose a bank auditor selects credit unions at random.
a. What is the probability that the second credit union selected will be the first to offer free checking?
b. What is the probability that the first credit union to offer free checking will be one of the first three?
c. Suppose the first credit union to offer free checking is the 10th selected. Is there any evidence to suggest that the claim (72%) is false? Justify your answer.