1. The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand. x Unit Demand 0 1,000 2,000 3,000 4,000 f(x) Probability 0.10 0.10 0.30 0.40 0.10 a. Determine the expected number of units demanded per month. b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units? 2. The probability distribution of the daily demand for a product is shown below. Demand 0 1 2 3 4 5 6 a. b. Probability 0.05 0.10 0.15 0.35 0.20 0.10 0.05 What is the expected number of units demanded per day? Determine the variance and the standard deviation. 3. The probability function for the number of insurance policies John will sell to a customer is given by f(X) = 0.5 - (X/6) for X = 0, 1, or 2 a. b. c. d. e. 4. Is this a valid probability function? Explain your answer. What is the probability that John will sell exactly 2 policies to a customer? What is the probability that John will sell at least 2 policies to a customer? What is the expected number of policies John will sell? What is the variance of the number of policies John will sell? The probability distribution for the rate of return on an investment is Rate of Return (In Percent) 9.5 9.8 10.0 10.2 10.6 a. b. c. Probability .1 .2 .3 .3 .1 What is the probability that the rate of return will be at least 10%? What is the expected rate of return? What is the variance of the rate of return? 2 5. The management of a grocery store has kept a record of bad checks received per day for a period of 200 days. The data are shown below. Number of Bad Checks Received 0 1 2 3 4 5 6 7 a. b. c. d. e. Number of Days 8 12 20 60 40 30 20 10 Develop a probability distribution for the above data. Is the probability distribution that you found in Part “a” a proper probability distribution? Explain. Determine the cumulative probability distribution F(x). What is the probability that in a given day the store receives four or less bad checks? What is the probability that in a given day the store receives more than 3 bad checks? 6. The following table shows part of the probability distribution for a random variable x. x 0 1 2 3 a. b. f(x) 0.2 ? 0.15 ? 4 0.15 The mean of the above distribution is known to be 1.8 (i.e., E(x) = 1.8). Determine f(1) and f(3). Compute the variance and the standard deviation for the above probability distribution. 3
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