Question: In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. If a binomial distribution applies, give the values of n and p.

a. Most calls made at random by sample surveys don’t succeed in talking with a live person, Of calls to New York City, only 1/12 succeed. A survey calls 500 randomly selected numbers in New York City. X is the number that reaches a live person.

b. At peak periods, 25% of attempted logins to an Internet service provider fail. Login attempts are independent and each has the same probability of failing. Darci logs in repeatedly until she succeeds. X is the umber of the login attempt that finally succeeds.

c. On a bright October day, Canada geese arrive to foul the pond at an apartment complex at the average rate of 12 geese per hour; X is the number of geese that arrive in the next three hours.