Hurricanes. In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability. Hurricanes a. Find the probability that in a year, there will be 7 hurricanes. b. In a 55-year period, how many years are expected to have 7 hurricanes? c. How does the result from part (b) compare to the recent period of 55 years in which 7 years had 7 hurricanes? Does the Poisson distribution work well here?

Complaints about an Internet brokerage firm occur at a rate of 4 per day. The number of complaints appears to be Poisson distributed. A. Find the probability that the firm receives 5 or more complaints in a day. Probability = B. Find the probability that the firm receives 10 or more complaints in a 3-day period. Probability =

The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 16-year period. Assume each year is independent. Part (a) Part (b) List the values that X may take on. X=0, 1, 2,..., 15, 16 OX= 1, 2, 3, OX= 1, 2, 3, OX=1,2,3,... 15, 16 98, 99, 100 Part (c) Give the distribution of X X-B 0.02 □ Part (d) How many audits are expected in a 16-year period? (Round your answer to two decimal places.) 0.32 audits Part (e) Find the probability that a person is not audited at all. (Round your answer to four decimal places.) Part (1) Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.