4) A lobster fisherman has 50 lobster traps. His daily catch is the total (in pounds) of lobster landed from these lobster traps. The total catch per trap is distributed normally with mean 30 pounds and standard deviation 5 pounds. Find the probability that the lobster fisherman has a daily mean catch of more than 32 pounds. 2) The distribution for the number of stolen cars per day in a certain city has a mean equal to 1.3 and a standard deviation equal to 1.7. A random sample of 30 days is observed, and the daily mean number of cars stolen for this sample is calculated. Find the probability that mean number of stolen cars is higher than 2.

1) According to the American Cancer Society's Cancer Facts & Figures, 2013-2014, "a woman living in the U.S. has a 12.3% lifetime risk of being diagnosed with breast cancer." Suppose a random sample of 60 women in the U.S. is studied. Let X represent the number who will be diagnosed with breast cancer. a) Find the mean and standard deviation for the number of women who will be diagnosed with breast cancer. b) What is the probability that less than 3 of the 60 women will be diagnosed with breast cancer?

3) The Census Bureau reports that 50.8% of the U.S. population is female. The Centers for Disease Control & Prevention (CDC) indicates that 18.1% of the U.S. population smokes cigarettes. Furthermore, the CDC states that given a person is female, there is a 15.8% chance that she smokes cigarettes. Consider a randomly selected person from the U.S.. The following events are defined: F: a person is female S: a person smokes cigarettes b) What is the probability that the selected person is a female or a smoker? c) What is the probability that the selected person is a female but not a smoker? d) If the selected person is a smoker, what is the probability that the person is female? e) Are being a female and being a smoker independent events? Support your answer appropriately.

4) An entry-level accountant is expected to work long hours during the accounting firm's "busy season". Let X be the number of hours per day an entry level accountant works. X can be described by a normal distribution with mean 12.9 hours and standard deviation 2.4 hours. a) Find the mean and standard deviation for the sampling distribution of an entry-level accountant's average daily hours for the month of January (31 days). b) What is the probability that the entry-level accountant's average number of hours worked per day for the month of January is between 12 and 14? c) What is the probability that the entry-level accountant worked more than 15 hours on any given day in January? d) How many hours does an entry-level accountant work during the longest 15% of days?