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10. A set of 50...

10. A set of 50 data values has a mean of 30 and a variance of 4.

I. Find the standard score (z) for a data value = 26.

II. Find the probability of a data value < 26.

III. Find the probability of a data value > 26.

Show all work.

11. Assume that the average annual salary for a worker in the United States is $37,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following:

(A) What percentage of Americans earn below $27,000?

(B) What percentage of Americans earn above $40,000?

Please show all of your work.

12. Answer the following:

(A) Find the binomial probability P(x = 6), where n = 12 and p = 0.30.

(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.

(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations

13. A sample of 84 golfers showed that their average score on a particular golf course was 87.79 with a standard deviation of 4.52.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 98% confidence interval of the mean score for all 84 golfers.

(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 84.

(C) Which confidence interval is smaller and why?

14. Assume that the population of heights of female college students is approximately normally distributed with mean mu of 66.45 inches and standard deviation (?) of 4.72 inches. A random sample of 82 heights is obtained. Show all work.

(A) Find p(x>65.5)

(B) Find the mean and standard error of the xbar distribution

(C) Find p(xbar>65.5)

(D) Why is the formula required to solve (A) different than (C)?

15. The diameters of apples in a certain orchard are normally distributed with a mean of 4.77 inches and a standard deviation of 0.43 inches. Show all work.

(A) What percentage of the apples in this orchard is larger than 4.71 inches?

(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.71 inches?

(C) What statistic is used to test (A) and (B) and why?

16. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:

(A)Ho: µ=79and Ha: µ?79, a = 0.01

(B)Ho: µ=53 and Ha: µ<53, a = 0.05

(C)Ho: µ=54 and Ha: µ>54, a = 0.10

17. Describe what a type I and type II error would be for each of the following null hypotheses:

: There is no good plan for the Iraq war.

18. A researcher claims that the average age of people who buy lottery tickets is 64. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 7. At alpha (a)

= 0.05 is there enough evidence to reject the researcher’s claim? Show all work.

49 63 80 52 22 80 72 56 70 56

24 46 70 74 70 61 65 71 39 74

79 76 71 49 62 68 71 67 69 45

19. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 95 hours.

I. Find the standard score (z) for a data value = 26.

II. Find the probability of a data value < 26.

III. Find the probability of a data value > 26.

Show all work.

11. Assume that the average annual salary for a worker in the United States is $37,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following:

(A) What percentage of Americans earn below $27,000?

(B) What percentage of Americans earn above $40,000?

Please show all of your work.

12. Answer the following:

(A) Find the binomial probability P(x = 6), where n = 12 and p = 0.30.

(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.

(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations

13. A sample of 84 golfers showed that their average score on a particular golf course was 87.79 with a standard deviation of 4.52.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 98% confidence interval of the mean score for all 84 golfers.

(B) Find the 98% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 84.

(C) Which confidence interval is smaller and why?

14. Assume that the population of heights of female college students is approximately normally distributed with mean mu of 66.45 inches and standard deviation (?) of 4.72 inches. A random sample of 82 heights is obtained. Show all work.

(A) Find p(x>65.5)

(B) Find the mean and standard error of the xbar distribution

(C) Find p(xbar>65.5)

(D) Why is the formula required to solve (A) different than (C)?

15. The diameters of apples in a certain orchard are normally distributed with a mean of 4.77 inches and a standard deviation of 0.43 inches. Show all work.

(A) What percentage of the apples in this orchard is larger than 4.71 inches?

(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.71 inches?

(C) What statistic is used to test (A) and (B) and why?

16. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:

(A)Ho: µ=79and Ha: µ?79, a = 0.01

(B)Ho: µ=53 and Ha: µ<53, a = 0.05

(C)Ho: µ=54 and Ha: µ>54, a = 0.10

17. Describe what a type I and type II error would be for each of the following null hypotheses:

: There is no good plan for the Iraq war.

18. A researcher claims that the average age of people who buy lottery tickets is 64. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 7. At alpha (a)

= 0.05 is there enough evidence to reject the researcher’s claim? Show all work.

49 63 80 52 22 80 72 56 70 56

24 46 70 74 70 61 65 71 39 74

79 76 71 49 62 68 71 67 69 45

19. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 95 hours.

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