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1. New Jersey Power Co. provides lower rates to customers that

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1. New Jersey Power Co. provides lower rates to customers that agree to use energy savings mainly at off-peak hrs. 30% of its customers take advantage of these savings. The consumer affairs department has conducted a focus group and is preparing to conduct a random telephone survey of 500 customers. The department supervisor wants to make sure that the group will contain a sufficient proportion of off-peak users. A. What is the probability of obtaining fewer than 150 off-peak users in the survey? B. What is the smallest number of off-peak users likely to be included in this sample? 2. The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated by Journal of Quality Technology. The quantity injected per container is approximate normally distributed with a mean of 10 units and a standard deviation of .2 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units is considered under-filled and must be reprocessed at a cost of $10. A properly filled container sells for $230 A. Find the probability that a container is under-filled? Not under-filled? B. A container is initially under-filled and must be reprocessed. Upon refilling it contains 10.6 units. How much profit will the company make on this container? C. The operations manager adjusts the mean of the filling process upward to 10.10 units in order to make the probability of under-filling approximately zero. Under these conditions what is the expected profit per container? 3. Assume that X us a binomial random variable with n=100 and p=.40. Use a mormal approximation to find the following A. X is less than or equal to 35 B. X is greater than or equal to 40 but less than or equal to 50 C. X is greater than or equal to 38 5. The Chronicle of Higher Education Almanac reports that the percentage of undergraduate in the United States receiving federal financial aid is 45% at public four-year institutions and 52% at private four-year institutions. The U.S. Department of Education is interested in questioning a random sample of 100 U.S. undergraduate students to assess its satisfaction with federal financial aid procedures and polices. A. Assume the appropriate percentage above applies to your institution. If a random sample of 100 students from your institution were contacted, what is the probability that 50 or more receive financial aid? Less than 25? 5. The distribution of the demand (in number of units per unit time) for a product can often be approximated by a normal probability distribution. For example: A baker has determined that the number of loaves of it’s white bread demanded daily has a normal distribution with a mean of 7,200 loaves and standard deviation of 300 loaves. Based on cost consideration, the company has decided that its best strategy is to produce a sufficient number of loaves so that it will fully supply demand on 94% of all days. A. How many loaves of bread should the company produce? B. Based on the production in part A., on what percentage of days will the company be left with more than 500 loaves of unsold bread?

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