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1.Consider a population with a...

1.Consider a population with a mean= 99.4 and standard deviation= 5.55.

(A)Calculate the z-score for /x= 97.3 from a sample of size 38.

Use the formula z = (xbar – miu) / (std dev / sqrt n)

(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 99% and a population standard deviation of 15, 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 = 93. Show all work.

3. A sample of 83 golfers showed that their average score on a particular golf course was 84.81 with a standard deviation of 5.99.

Answer each of the following (show all work)

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

(A) Find the 90% confidence interval of the mean score for all 83 golfers.

(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 83.

(C) Which confidence interval is larger and why?

4. Assume that the population of heights of female college students is approximately normally distributed with mean m of 68.42 inches and standard deviation s of 6.34 inches. A random sample of 73 heights is obtained. Show all work.

(A)Find the mean and standard error of the /x distribution.

(B)Find P(/x>67.75)

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?

So far I have this, but I’m not sure if this is right and how to finish:

Z=5.36-5.44/0.41=-0.08/0.41= -0.1951 P(z>-0.1951)= 1-

(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 4.18, how large a sample is needed to get the desired information to be accurate within 0.64 decibels? Show all work.

Use the formula for n= (Zalpha/2 x standard dev. / E)^2

(A)Calculate the z-score for /x= 97.3 from a sample of size 38.

Use the formula z = (xbar – miu) / (std dev / sqrt n)

(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 99% and a population standard deviation of 15, 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 = 93. Show all work.

3. A sample of 83 golfers showed that their average score on a particular golf course was 84.81 with a standard deviation of 5.99.

Answer each of the following (show all work)

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

(A) Find the 90% confidence interval of the mean score for all 83 golfers.

(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 83.

(C) Which confidence interval is larger and why?

4. Assume that the population of heights of female college students is approximately normally distributed with mean m of 68.42 inches and standard deviation s of 6.34 inches. A random sample of 73 heights is obtained. Show all work.

(A)Find the mean and standard error of the /x distribution.

(B)Find P(/x>67.75)

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?

So far I have this, but I’m not sure if this is right and how to finish:

Z=5.36-5.44/0.41=-0.08/0.41= -0.1951 P(z>-0.1951)= 1-

(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 4.18, how large a sample is needed to get the desired information to be accurate within 0.64 decibels? Show all work.

Use the formula for n= (Zalpha/2 x standard dev. / E)^2

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