A particular automobile costs an average of $21,755 in the Pacific Northwest. The standard deviation of prices is $650. Suppose a random sample of 40 dealerships in Washington and Oregon is taken and their managers are asked what they charge for this automobile. What is the probability of getting a sample average cost of less than $21,500? Assume that only 120 dealerships in the entire Pacific Northwest sell this automobile.
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A particular automobile costs an average of $21,755 in the Pacific Northwest. The standard deviation of prices is $650. Suppose a random sample of 40 dealerships in Washington and Oregon is taken and their managers are asked what they charge for this automobile. What is the probability of getting a sample average cost of less than $21,500? Assume that only 120 dealerships in the entire Pacific Northwest sell this automobile.
(Round z values to 2 decimal places, e.g. 0.75. Round all intermediate calculation and answers to 4 decimal places, e.g. 0.7571.)
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- Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poors 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another way to look at it that shows that Balboas beating the market 11 out of 13 times is not unusual. Consider 50 mutual funds, each of which has a 50% chance of beating the market during a given year. Use simulation to estimate the probability that over a 13-year period the best of the 50 mutual funds will beat the market for at least 11 out of 13 years. This probability turns out to exceed 40%, which means that the best mutual fund beating the market 11 out of 13 years is not an unusual occurrence after all.
- Suppose you were preparing two-way tables of percentages for the following pairs of variables. How would you run the percentages? Crime rate and unemployment rateNew York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)? c. What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimals)? d. What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar. or - Select your answer - ♥You have been pricing Samsung-Galaxy SmartWatch in several stores. Three stores have the identical price of $400. Each store charges 18 percent APR, has a 30-day grace period, and sends out bills on the first of the month. On further investigation, you find that store A calculates the finance charge by using the average daily balance method, store B uses the adjusted balance method, and store C using the previous balance method. Assume you purchased the SmartWatch on May 5 and made a $100 payment on June 15. What will the finance charge for June be if you made your purchase from store A?
- You have been pricing Samsung-Galaxy SmartWatch in several stores. Three stores have the identical price of $600. Each store charges 12 percent APR, has a 30-day grace period, and sends out bills on the first of the month. On further investigation, you find that store A calculates the finance charge by using the average daily balance method, store B uses the adjusted balance method, and store C using the previous balance method. Assume you purchased the SmartWatch on May 5 and made a $100 payment on June 15. What will the finance charge for June be if you made your purchase from store A? From store B? From store C?ou have been pricing Samsung-Galaxy SmartWatch in several stores. Three stores have the identical price of $400. Each store charges 18 percent APR, has a 30-day grace period, and sends out bills on the first of the month. On further investigation, you find that store A calculates the finance charge by using the average daily balance method, store B uses the adjusted balance method, and store C using the previous balance method. Assume you purchased the SmartWatch on May 5 and made a $100 payment on June 15. What will the finance charge for June be if you made your purchase from store A? From store B? From store C?The following table shows the number of televisions sold over the last ten years at a local electronic store. YEAR TV SALES 1 150 2 300 3 480 4 600 5 630 6 640 7 700 8 825 9 900 10 980 Using trend projection, develop a formula to predict sales for years 11 and 12. You have to show all working. You will need to develop a table to calculate the slope and the intercept. Use that formula to forecast television sales for years 11 and 12.
- You wish to estimate the mean number of travel days per year for salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 38 days.If you want to estimate the population mean with 95% confidence and a margin of error of 9 days, how many salespeople should you sample?(Use t Distribution Table & z Distribution Table.) (Round z value to 3 decimal places and round your answer to the next whole number.) What is the number of salespeople to be sampled?is selling Christmas trees. She purchases trees for $10 and sells for $25 each. The number of trees she can sell is normally distributed with a mean of 100 and standard deviation of 30. How many trees should purchase?The following table shows the number of televisions sold over the last ten years at a local electronic store. Year TV Sales 1. 150 2. 300 3. 480 4. 600 5. 630 6. 640 7. 700 8. 825 9. 900 10. 980 Using trend projection, develop a formula to predict sales for years 11 and 12. You have to show all working. You will need to develop a table to calculate the slope and the intercept. [9 marks] 2. Use that formula to forecast television sales for years 11 and 12. [2 marks]