A politician believes that 20% of all macroeconomists in senior positions will strongly support a proposal he wishes to advance. Suppose that this belief is correct and that five senior macroeconomists are approached at random. 

What is the probability that at least one of the five will strongly support the proposal?

A campus finance officer finds that, for all parking tickets issued, 78% of fines are paid. The fine is $2. 

In the most recent week 620 parking tickets have been issued. 

Find the mean of the amount of money that will be obtained from the payment of these fines. 

A student answers an online multiple-choice quiz until they have answered incorrectly three times. The questions get progressively harder, so the probability of answering incorrectly increases with each question.

Is it appropriate to model the number of questions answered until the student makes three incorrect answers as a negative binomial random variable? Select all that apply:

Suppose we know that births in a hospital occur randomly at an average rate of

1.3 births per hour.

What is the probability that we observe 10 births in a given 4 hour interval? Write your answer with 2 decimal places.

In a negative binomial distribution, the number of failures is fixed, and the number of trials varies until the required number of successes is achieved.

In a certain Kentucky Fried Chicken franchise, half of the customers request "crispy" instead of "original", on average. 

What is the probability of serving more than 6 customers until the first request for "crispy"?

If X is a binomial random variable X ~ bin(n, p = 0.5), then the mean of X will equal its median.

In a large city, telephone calls to 911 come on the average of 2 calls every 3 minutes. If one assumes an approximate Poisson process, what is the probability of five or more calls arriving in a 9-minute period?

Assume that 40% of candidates who sit for the CFA examination pass it the first time. Of a random sample of 15 candidates who are sitting for the exam for the first time, what is the expected number of candidates that will pass?