1. On average, 2.9 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?

2. A travelling salesman sells milkshake mixing machines and on average sells 8.7 machines per month. He needs to sell at least 3 machines each month order to stay in business, otherwise he will shut down. Using the Poisson distribution, what is the probability he will have to shut down after this month?

3. A light bulb factory produces 791 light bulbs every hour. Approximately 1.86% of the light bulbs are defective, and do not work. Using the binomial distribution, what is the expected number of defective bulbs produced in an hour?

4. A light bulb factory produces 635 light bulbs every hour. Approximately 1.45% of the light bulbs are defective, and do not work. Using the binomial distribution, what is the standard deviation of the number of defective bulbs produced in an hour?

5. A call center receives an average of 11.5 calls per hour. Assuming the number of calls received follows the Poisson distribution, what is the variance in the number of calls per hour?

6. Suppose you toss a six-sided die 14 times. What is the probability of never rolling a 2?

7. In 2018 there were 428,267 total motor vehicle crashes in Freedonia. Assuming that number reflects the true average now and that it follows the Poisson distribution, what is the probability that at least one accident will occur somewhere in the state of Freedonia in the next minute? Hint: There 525,600 minutes in a year.

8. A call center receives an average of 11 calls per hour. Assuming the number of calls received follows the Poisson distribution, determine the probability would receive exactly 20 calls in a given hour.