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σ = 5.63. (A) Calculate...

1. Consider a population with mean μ = 77.6 and(Standard Deviation) σ = 5.63.

(A) Calculate the z-score for x̅ = 76.1 from a sample of size 52.

(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?

2. Given a level of confidence of 95% and a population standard deviation of 9, answer the following:

(A) What other information is necessary to find the sample size (n)?

(B) Find the Maximum Error of Estimate (E) if n = 72. Show all work.

3. A sample of 82 golfers showed that their average score on a particular golf course was 81.93 with a standard deviation of 3.87.

Answer each of the following (show all work

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

(A) Find the 99% confidence interval of the mean score for all 82 golfers.

(B) Find the 99% confidence interval of the mean score for all golfers if this is a sample of 145 golfers instead of a sample of 82.

(C) Which confidence interval is smaller and why?

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

(A) Find the mean and standard error of the x̅ distribution

(B) Find P( x̅ > 65.50)

5. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.44 inches and a standard deviation of 0.41 inches. Show all work.

(A) What percentage of the grapefruits in this orchard is larger than 5.36 inches?

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.36 inches?

6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.19, how large a sample is needed to get the desired information to be accurate within 0.54 decibels? Show all work.

(A) Calculate the z-score for x̅ = 76.1 from a sample of size 52.

(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?

2. Given a level of confidence of 95% and a population standard deviation of 9, answer the following:

(A) What other information is necessary to find the sample size (n)?

(B) Find the Maximum Error of Estimate (E) if n = 72. Show all work.

3. A sample of 82 golfers showed that their average score on a particular golf course was 81.93 with a standard deviation of 3.87.

Answer each of the following (show all work

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

(A) Find the 99% confidence interval of the mean score for all 82 golfers.

(B) Find the 99% confidence interval of the mean score for all golfers if this is a sample of 145 golfers instead of a sample of 82.

(C) Which confidence interval is smaller and why?

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

(A) Find the mean and standard error of the x̅ distribution

(B) Find P( x̅ > 65.50)

5. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.44 inches and a standard deviation of 0.41 inches. Show all work.

(A) What percentage of the grapefruits in this orchard is larger than 5.36 inches?

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.36 inches?

6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.19, how large a sample is needed to get the desired information to be accurate within 0.54 decibels? Show all work.

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