1. [10 points] For a standard normal distribution. Find the indicated probability. For each case, draw a sketch. (a). (3 points) P( z < 152.

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1 Spring 2007 Math 227 Test #3 Name: Show all necessary work NEATLY, UNDERSTANDABLY and SYSTEMATICALLY for full points. Any understatement and/or false statement may be penalized. This is a closed book, closed note and closed neighborhood test. If you are using a TI calculator, you must write down exactly what was input to the calculator. Total is 110 points. Good Luck! 1. [10 points] For a standard normal distribution. Find the indicated probability. For each case, draw a sketch. (a). (3 points) P( z < 152. ) (b). (4 points) P( 015. < z < 134. ) (c). (4 points) P( z > ) 2. [6 points] The Labor Bureau wants to estimate, at a 98% confidence level, the proportion of all households that receive welfare. A preliminary sample showed that 18% of households in this sample receive welfare. Find the sample size that would limit the maximum error of estimate to within 0.05 of the population proportion.

2 3. [8 points] A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects. [4 points] Critical values: [4 points] Confidence interval: 4. [12 points] In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said that they used the Internet for shopping at least a few times a year. (a). [3 points] Find the point of estimate of the percentage of adults who use the Internet for shopping. (b). Find a 99% confidence interval estimate of the percentage of adults who use the Internet for shopping. [3 points] Critical value: [3 points] Margin of Error: [3 points] Confidence Interval:

3 5. [6 points] A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours. 6. [14 points] The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The time (in minutes) were: 6, 15, 4, 11, 10, 5, 7, 9, 12, 7. Find a 98% confidence interval for the population mean. Assume the population is normally distributed. [1 point] Sample size: [2 points] Sample mean: [2 points] Sample Standard Deviation: [3 points] Critical value: [3 points] Margin of Error: [3 points] Confidence Interval: 7. [6 points] MTA reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Use the normal approximation to the binomial to approximate the probability that 38 or fewer arrive on time. Mean: Standard Deviation:

4 8. (a).[5 points] Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P( z > c) = 01093,. find c. (b). [5 points] Scores on an English test are normally distributed with a mean of 30.6 and a standard deviation of 6. Find the score that separates the top 59% from the bottom 41% 9. [6 points] An alumni association wants to estimate the mean debt of this year s college graduates. It is known that the population standard deviation of the debts of this year s college graduates is $11,800. How large a sample should be selected so that the estimate with a 99% confidence level is within $800 of the population mean? 10. [12 points] A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of all such textbooks in the market. The research department at the company took a sample of 36 comparable textbooks and collected information on their prices. This information produced a mean price of $70.50 and standard deviation of $4.50 for this sample. Construct a 90% confidence interval for the mean price of all such college textbooks. [3 points] Point of estimate: [3 points] Critical value: [3 points] Margin of error: [3 points] The 90% confidence interval:

5 11. [8 points] Assume that women s weights are normally distributed with a mean of 135 pounds and a standard deviation of 15 pounds. (a). (4 points) If one woman is randomly selected, find the probability that her weight is more than 114 pounds. (b). (4 points) If 36 women are randomly selected, find the probability that they have a mean weight more than 114 pounds. 12. [12 points] One survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke and 641 do not smoke. Use a 0.02 significance level to test the claim that the rate of smoking among those with four years of college is less than 27% rate for the general population.