Exam 9: Random Variables and Probability Distributions

The probability model for random variable X is specified as: P(X) = X/6 for X = 1, 2 or 3 The expected value of X is

The city of Halifax has determined that the time between arrivals at a toll booth at the Angus L. Macdonald Bridge is exponentially distributed with λ = 4 cars per minute. Based on this information, what is the probability that the time between any two cars arriving will exceed 11 seconds?

Consider the following to answer the question(s) below: A company believes that there will be a 50% chance of making a profit of $1,000, a 30% chance of making a profit of $1500 and a 20% chance of making a profit of $2,000. -What is the expected profit?

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a Normal model with a mean of 22 minutes and a standard deviation of four minutes. a. What percent of new machine set ups take more than 30 minutes? b. The typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of new machine set ups are completed within 25 minutes to allow for this?

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines on a given day. a. On one day he had 280 customers. Assuming this day was typical, what would be the mean and standard deviation of the number of customers who buy magazines each day? b. Surprised by the high number of customers who purchased magazines that day, the owner decided that his 5% estimate must have been too low. How many magazine sales would it have taken to convince you? Justify your answer.

A shareholder believes that in one year, there is a 20% chance that his stock will be worth $75, a 50% chance that it will be worth $100, and a 30% chance that it will be worth $140. a. Find the stock's expected value in one year. b. Find the standard deviation of the stock's worth in one year.

A company believes that there is a 25% chance of making a daily profit of $500, a 35% chance that it will be $1000 and 40% chance that it will be $1500. a. Find the expected value. b. Find the standard deviation.

Consider the following to answer the question(s) below: The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5 minute period, -Find the expected value.