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: Letbe 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: Letbe the number of people that donate their time to community projects, out of the sample of 15 people. Thenhas a Binomial distribution with parametersand. 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: Letbe 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: Letbe the minutes the bus is late, andhas 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:
Mean: 20.5 ozs.
Standard deviation: 0.2 oz.
What proportion of the 20 oz bags contain more than the advertised 20 ozs.?
Solution: Letbe the amount of corn chips. Then