### Probability Distributions & Sampling

Probability Distributions & Sampling You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock has the following probability distribution. Stock X Stock Y 1. (6 points) Compute the expected return for each stock. Show your calculation 2. (4 points) What stock is preferred for the objective of maximizing the expected profits? A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group (USA Today). Consider a random sample of 6 international travelers. 3. (5 points) MINITAB probability table (must be included to receive credit for 4 & 5) 4. (5 points) What is the probability that at least 2 will stick with their tour? 5. (5 points) What is the probability that none will stick with their tour? 6. (5 points) How many international travelers do you expect will stick with their tour? Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson variable with a mean of 2.4 per day. What is the probability that in any given day 7. (5 points) no network errors will occur? 8. (5 points) at most one network error will occur? ￼￼￼State of The Economy ￼￼x ￼￼￼￼P(x) ￼￼￼Recession ￼￼-50 ￼￼￼￼0.1 ￼￼￼Stagnation ￼￼20 ￼￼￼￼0.3 ￼￼￼Low – Moderate growth ￼￼￼￼100 ￼￼￼￼￼0.4 ￼￼￼High growth ￼￼￼150 ￼￼￼0.2 ￼￼￼￼￼￼State of The Economy ￼￼x ￼￼￼￼P(x) ￼￼￼Recession ￼￼-100 ￼￼￼￼0.1 ￼￼￼Stagnation ￼￼50 ￼￼￼￼0.3 ￼￼￼Low – Moderate growth ￼￼130 ￼￼￼￼0.4 ￼￼￼High growth ￼￼￼200 ￼￼￼￼0.2 ￼Summer ￼Silver Star, Inc. has a number of stores in major metropolitan shopping centers. The company’s sales experience indicates that daily cell phone sales in its stores follow a normal distribution with a mean of 60 and a standard deviation of 15. The marketing department conducts a number of routine analyses of sales data to monitor sales performance. 9. (10 points) What proportion of store sales days will have sales between 85 and 95 given that sales are following the historical experience? 10. (10 points) Find the cutoff point for the top 10% of all daily sales. Suppose that 50% of all adult Americans believe that they are unable to stop thinking about work while on vacation. 11. (10 points) What is the probability that more than 56% of a random sample of 150 adult Americans would hold this belief? 12. (5 points) If the sample of 150 was made up of adults randomly selected from each of the eight regions of the U.S. (i.e. New England, Midwest, Great Lakes, Plains, Southeast, Southwest, Rocky Mountains and Far West) which sampling design was used? Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of its testing program Sony tests samples of 25 batteries. 13. (10 points) What is the probability the sample will have a mean useful life between 34.5 and 36.0 hours? 14. (10 points) What is the probability the sample will have a mean useful life of more than 36 hours? 15. (5 points) Increasing the sample size causes the sampling distribution of x to ________. a) shift to the right b) shift to the left c) have more dispersion d) have less dispersion e) stay unchanged ￼Summer

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