1. The number of babies born during an 8-hour shift at a hospital follows a Poisson distribution.

Mean: 6 an hour

Find probability that 5 babies are born during a particular 1-hour period.

**Solution: **Let_{}be the number of babies born, then_{}. Then,

_{}

2. **0.3 of the general** population donate their time and energy to working on community projects. If 15 people have been randomly sampled from a community and asked if they donated their time and energy to community projects. Let x be the number of them that do donate their time an energy to community projects. Find the Probability that more than 5 of the 15 do donate their time and energy to community projects.

**Solution: **Let_{}be the number of people that donate their time to community projects, out of the sample of 15 people. Then_{}has a Binomial distribution with parameters_{}and_{}. Then, the probability we are looking for is equal to

_{}

3 The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 9.4. Find the probability that less than two accidents will occur on this stretch of road during a randomly selected month.

**Solution: **Let_{}be the number of traffic accidents, then_{}. The probability we are looking for is

_{}

4. A bus is scheduled to stop every 30 mins. The length of time that a bus is uniformly distributed and the maximum time a bus is late is 20 mins. What is the probability that the last bus on a given day will be more than 14 mins. late?

**Solution: **Let_{}be the minutes the bus is late, and_{}has uniform distribution_{}. The probability that the last bus on a given day will be more than 14 minutes late is

_{}

5. The amount of corn chips dispensed into a 20-ounce bag by the dispensing machine with a:

Normal distribution

Mean: 20.5 ozs.

Standard deviation: 0.2 oz.

What proportion of the 20 oz bags contain more than the advertised 20 ozs.?

**Solution: **Let_{}be the amount of corn chips. Then

_{}