Fifteen lobstermen have their boats anchored at a small pier along the New Hampshire coast. Five of these lobstermen have been fined within the past year for commercial lobster-size violations. Suppose four lobstermen are selected at random.
a. What is the probability that exactly two have been fined for violations within the past year? Write a Solution Trail for this problem.
b. What is the probability that all four have been fined for violations within the past year?
c. What is the probability that at least one has been fined for violations within the past year?
Buchtal, a manufacturer of ceramic tiles, reports 3.9 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. Suppose a year is selected at random.
a. What is the probability that there will be no job-related accidents?
b. What is the probability that the number of accidents that year will be between two and five (inclusive)?
c. If the number of accidents is more than three standard deviations above the mean, the company insurance carrier will raise the rates. What is the probability of an increase in the company’s insurance bill?
Amusement park rides are great family fun, but over 4400 children are injured on rides every year. According to a recent study, on average, one child is treated in a hospital Emergency Room every two hours as a result of an injury from an amusement park ride.Suppose a two-hour period is selected at random.
a. What is the probability that no children will be treated in an Emergency Room as a result of an injury from an amusement park ride?
b. What is the probability that at most three children will be treated in an Emergency Room as a result of an injury from an amusement park ride?
c. Suppose that six children are treated in an Emergency Room as a result of an injury on an amusement park ride. Is there any evidence to suggest that the claim (of one every two hours) is wrong? Justify your answer.