Name: ___________________
Directions: (a) Enter all your answers into this Word document in the space immediately following each question and submit the entire document. IMPORTANT: The name of your Word document MUST begin with your LAST NAME. (b) SHOW ALL YOUR WORK/calculations or results from a template. When you use a template to calculate an answer, copy and paste the results into this document. (c) While putting your answers in a different color font is helpful, please DO NOT use red font since this is the color used to provide feedback on your answers.
1. Scores on a college entrance examination are normally distributed with a mean (µ) of 500 and a standard deviation (σ) of 100. One college gives priority acceptance to students scoring above 650. What percentage of students is eligible for priority acceptance?
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2. Assume that weights of newborn children are normally distributed with a mean (µ) of 116 ounces and a standard deviation (σ) of 12 ounces. Find the upper and lower limits that separate the top 5% and the bottom 5%.
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3. On one I.Q. test, the mean score (µ) is 100 and the population standard deviation (σ) is 15. A sample of 50 scores is selected from a very large population. Find the probability that the mean of the sample group is more than 103.
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4. The manager of Cardinal Electric's light bulb division must estimate the average number of hours that a light bulb made by each light bulb machine will last. A sample of 40 light bulbs was selected from machine A and the average burning time (x̄̄) was 1,416 hours. The standard deviation (σ) of burning time is known to be 30 hours. Construct a 90 percent confidence interval for the true population mean.
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5. Northern Orange County has found that the population has a severe problem with dental plaque. Every year the local dental board examines a sample of patients and rates each patient's plaque buildup on a scale from 1 to 100, with 1 representing no plaque and 100 representing a great deal of plaque. This year, the board examined 21 patients and found that they had an average (x̄̄) Plaque Rating Score (PRS) of 72 and a standard deviation (s) of 6.2. Construct a 98 percent confidence interval for the mean PRS for Northern Orange County.
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6. Atlas Sporting Goods has implemented a special trade promotion for its propane stove and feels that the promotion should result in a price decrease for the consumer. Atlas knows that before the promotion began, the average retail price (µ) of the stove was $44.95, and the standard deviation (σ) was $5.75. Atlas samples 25 of its retailers after the promotion begins and finds the mean price for the stoves (x̄) is now $42.95. At a 0.02 significance level, does Atlas have reason to believe that the average retail price to the consumer has decreased?
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7. From 1980 until 1985, the mean (μ) price/earnings (P/E) ratio of the approximately 1,800 stocks listed on the New York Stock Exchange was 14.35 and the population standard deviation (σ) was 9.73. In a sample of 30 randomly chosen NYSE stocks, the mean P/E ratio in (x̄) 1986 was 11.77. Does the sample present sufficient evidence to conclude (at the 0.05 level of significance) that in 1986 the mean P/E ratio for NYSE stocks had changed from its earlier value?
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