for each problem: a) Identify whether the best distribution to solve the problem is Binomial, Poisson, or Exponential. b) Identify the correct value of all defining parameters. c) Find the indicated probability to 4 decimal places. Seven people are randomly interviewed from a large population that is 55% female. Assuming independence, find the probability that exactly 4 of the selected people are women. 2) A website has an average of 4 hits per minute. In a 4-minute period, what is the probability that it gets exactly 9 hits? 3) In the previous problem, we can see that, on average, the time between hits is 15 seconds. What is the probability that 30 seconds or more goes by between hits? 4) Assume that each person entering the Apple store has a 30$ chance of making a purchase. Suppose that 11 potential customers enter the store. Assuming independence, find the probability that fewer than 5 of them make purchases. A salesman notes that his success rate is about 15$. If he has 20 customers, and assuming independence, find the probability that he makes exactly 2 sales. 6) A certain kind of light bulb lasts 1 year on average. What is the probability that a given light bulb will fail in less than a year? 7) Suppose that the expected number of customers at a convenience store is 6 every 20 minutes. In a given 20-minute time period, find the probability of having more than 5 customers. 8) Find the probability that an investor makes a profit on 7 of her next 14 investments, assuming independence and a 0.6 chance of making a profit each time