1.. The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 62, find the probability of a sample mean being less than 19.6 if mu equals20 and sigma equals1.22.

For a sample of n equals 62, the probability of a sample mean being less than

19.6 if mu equals 20and sigma equals1.22 is

. (Round to four decimal places as needed.)

2. The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of N equals 65

, find the probability of a sample mean being greater than 223 if mu equals 222 and sigma equals 5.6. For a sample of N equals 65

, the probability of a sample mean being greater than 223 if mu equals 222 and sigma equals5.6

is

.

(Round to four decimal places as needed.)

3. Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.706 per gallon. A random sample of 35 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.696 and $2.728 that week ? Assume sigma equals$0.045.

The probability that the sample mean was between $2.696 and $2.728 is

(Round to four decimal places as needed.)

4. Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of

9 feet (108 inches) with a standard deviation of

0.6inch. Assume the lengths are normally distributed. You randomly select 37 boards and find that the mean length is 108.29 inches. Complete parts (a) through (c).

(a) Assuming the seller’s claim iscorrect, what is the probability that the mean of the sample is

108.29 inches or more?

(Round to four decimal places as needed.)

5. Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability.In a sample of 700 gas stations, the mean price for regular gasoline at the pump was $ 2.862per gallon and the standard deviation was $0.008per gallon. A random sample of size 50is drawn from this population. What is the probability that the mean price per gallon is less than $2.859? The probability that the mean price per gallon is less than $2.859

is (Round to four decimal places as needed.)

.

6. Find the critical value z Subscript c necessary to form a confidence interval at the level of confidence shown below. C equals 0.89 z Subscript c equals

(Round to two decimal places as needed.)

8. Find the critical value z Subscript c necessary to form a confidence interval at the level of confidence shown below. C equals 0.92 z Subscript c equals

(Round to two decimal places as needed.)

9. Find the margin of error for the given values of c, sigma , and n.cequals0.95, sigma equals 3.2, n equals 81.

Level of Confidence z Subscript c

90% 1.645

95% 1.96

99% 2.575

E=

(Round to three decimal places as needed.)

10. Construct the confidence interval for the population mean mu c equals

0.98, x overbar equals 16.3, sigma equals 8.0, and n equals 5 .

A 98% confidence interval for mu is left parenthesis nothing comma nothing right parenthesis .

(Round to one decimal place as needed.)

11.Use the confidence interval to find the margin of error and the sample mean.(1.67,1.95).

The margin of error is

.

(Round to two decimal places as needed.)

12. Find the minimum sample size n needed to estimate mu for the given values of c, sigma

, and E.c equals 0.98, sigma equals 5.7, and E equals 2.Assume that a preliminary sample has at least 30 members. N equals

(Round up to the nearest whole number.)

13. People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 99% confidence? Initial survey results indicate that sigma equals 16.6 books.

A 99 % confidence level requires subjects.

(Round up to the nearest whole number as needed.)

14. A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 3 points with 99 % confidence assuming sigma equals 16.5 question mark Suppose the doctor would be content with 90 %

confidence. How does the decrease in confidence affect the sample size required?

A 99% confidence level requires

subjects.

(Round up to the nearest whole number as needed.)

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