# 5.5 The number of arrivals per minute at a bank located in the central business

5.5 The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results: a. Compute the expected number of arrivals per minute. b. Compute the standard deviation. 5.9 Determine the following: a. For n=4 and p=0.12, what is P1X=02? b. For n=10 and p=0.40, what is P1X=92? c. For n=10 and p=0.50, what is P1X=82? d. For n=6 and p=0.83, what is P1X=52? 5.15 Past records indicate that the probability of online retail or-ders that turn out to be fraudulent is 0.08. Suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. a. What are the mean and standard deviation of the number of on-line retail orders that turn out to be fraudulent? b. What is the probability that zero online retail orders will turn out to be fraudulent? c. What is the probability that one online retail order will turn out to be fraudulent? d. What is the probability that two or more online retail orders will turn out to be fraudulent? 5.21 Assume that the number of new visitors to a website in one hour is distributed as a Poisson variable. The mean number of new visitors to the website is 4.0 per hour. What is the probability that in any given hour. a. zero new visitors will arrive at the website? b. exactly one new visitor will arrive at the website? c. two or more new visitors will arrive at the website? d. fewer than three new visitors will arrive at the website? 5.25 The U.S. Department of Transportation maintains statistics for involuntary denial of boarding. In July–September 2013, the American Airlines rate of involuntarily denying boarding was 0.45 per 10,000 passengers. What is the probability that in the next 10,000 passengers, there will be. a. no one involuntarily denied boarding? b. at least one person involuntarily denied boarding? c. at least two persons involuntarily denied boarding?