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# Statistics Problems

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8. Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of \$34,000 and standard deviation of \$2000. What is the cutoff salary for teachers in the bottom 10%?

9. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. If 36 women are randomly selected, find the probability that they have a mean pregnancy between 267 days and 269 days.

12. In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30 minutes.

13. In a survey of 2480 golfers, 15% said they were left-handed. The survey's margin of error is 3%. Construct a confidence interval for the portion of left-handed golfers.

15. You wish to test the claim that mu = 1200 at a level of significance of alpha=0.01 and are given sample statistics n=35, sample mean = 1170 and s=82. Compute the value of standardized test statistic. Round your answer to two decimal places.

17. Suppose you want to test the claim that mu is greater than 25.6. Given a sample size of n=42 and a level of significance of alpha=0.1, when should you reject Ho?

23. A manager gathered data to determine a relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars). The data is shown in the table.

Miles (x) 2 3 10 7 8 15 3 1 11
Sales (y) 31 33 78 62 65 61 48 55 120

He used statistical regression to find the line of best fit. The line equation was found to be y=3.529x + 37.916. Predict the sales for travel of 800 miles.

24. Use the given frequency distribution to find the
(a) class width
(b) class midpoints of the first class
(c) class boundaries of the first class.

Weight (in pounds)
Class Frequency (f)
135-139 6
140-144 4
145-149 11
150-154 15
155-159 8