Probability & Decision Making under Uncertainty,
Normal, Binomial, Poisson, and Exponential Distributions
Study Activities
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Activity 1:
For this weeks discussion describe to your class mates a business problem where you might use a binomial distribution and one where you would use a Poisson distribution. Then explain why you would use one over the other, i.e. advantages and disadvantages of using one or the other.
Activity Outcomes
1. Recognizing the limitations and assumptions of the data or statistical technique .
2. Evaluate course concepts critically and competently through interaction with Learners and Faculty Mentor.
Activity 2:
Exercise Problems
Activity Description
Exercise Problems
For this assignment complete the exercises below. Show enough of your work so that your instructor can follow your logic.
Question 1: (Pg 204) In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions about X, the number of customers who will buy life insurance from this agent in the coming month:
a. What is the probability X is exactly 5?
b. What is the probability that X is no more than 10?
c. What is the probability that X is at least 20?
d. Determine the mean and standard deviation of X.
e. What is the probability that X will be within two standard deviations of the mean?
f. What is the probability that X will be within three standard deviations of the mean?
Question 2: Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. As major airline companies do, this hotel has adopted an overbooking policy in an effort to maximize the usage of its available lodging capacity. Assume that each potential hotel customer holding a room reservation, independently of other customers, cancels the reservation or simply does not show up at the hotel on a given night with probability 0.15.
a. Find the largest number of room reservations that this hotel can book and still be at least 95? sure that everyone who shows up at the hotel will have a room on a given night.
b. Given that the hotel books the number of reservations found in part a, find the probability that at least 90% of the available rooms will be occupied on a given night.
c. Given that the hotel books the number of reservations found in part a, find the probability that at most 80% of the available rooms will be occupied on a given night.
d. How does your answer to part a change as the required assurance rate increases from 95% to 97%?How does your answer to part a change as the required assurance rate increases from 95% to 99%?
e. How does your answer to part a change as the cancellation rate varies between 5% and 25% (in increments of 5%)? Assume now that the required assurance rate remains at 95%.
Question 3: The annual number of industrial accidents occurring in a particular manu?acturing plant is known to follow isson distribution with mean 12.
a. What is the probability of observing exactly 12 accidents during the coming year?
b. What is the probability of observing no more than 12 accidents during the coming year?
c. What is the probability of observing at least 15 accidents during the coming year?
d. What is the probability of observing between 10 and 15 accidents (inclusive) during the coming year?
e. Find the smallest integer k such that we can be at least 99% sure that the annual number of accidents occurring will be less than
Question 4: The daily demand for six-packs of Coke at Mr. D's supermarket follows a normal distribution with mean and standard deviation 30. Every Monday the Coke delivery driver delivers Coke to Mr. D's. If Mr. D's wants to have only a 1% chance of running out of Coke by the end of the week, how many should Mr. D's order for the week? Assume orders are placed on Sunday at midnight. Also assume that demands on different days are probabilistically independent.