08 Oct Scores on a college entrance examination are normally distributed with a mean (µ) of 500 and a standard deviation (σ)of 100.

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?[10 POINTS]

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%.[15 POINTS]

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.[15 POINTS]

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 (x??) 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.[15 POINTS]

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 (x??) 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.[15 POINTS]

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 (x?) 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?[15 POINTS]

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 (x?) 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?[15 POINTS]