1.A normal population has a mean of 58 and a standard deviation of 20. You select a random sample of 14. Use Appendix B.1 for the z values. Compute the probability that the sample mean is: (Round the final answers to 4 decimal places.)

a. Greater than 61. Probability

b. Less than 54. Probability

c. Between 54 and 61. Probability

CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 150 seconds (2 minutes and 30 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows a normal distribution with a standard deviation of nine seconds. Suppose that we select a sample of 12 cuts from various CDs sold by CRA CDs Inc. Use Appendix B.1 for the z values.

a. What can we say about the shape of the distribution of the sample mean?

Shape of the distribution is (Click to select) Normal Uniform Binomial

b. What is the standard error of the mean? (Round the final answer to 2 decimal places.)

Standard error of the mean seconds.

c. What percentage of the sample means will be greater than 157 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.)

Percentage %

d. What percentage of the sample means will be greater than 145 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.)

Percentage %

e. What percentage of the sample means will be greater than 145 but less than 157 seconds? (Round the z values to 2 decimal places and the final answers to 2 decimal places.)

Percentage %

3.

A recent study by the Island Resort Taxi Drivers Association showed that the mean fare charged for service from the beach to the airport is $34 and the standard deviation is $6.5. We select a sample of 11 fares. Use Appendix B.1 for the z-values.

a. What is the likelihood that the sample mean is between $32 and $37?(Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Probability

b. What must you assume to make the above calculation?

(Click to select) Assume the population is normally distributed. Assume the population is uniformly distributed. Assume the population is not normally distributed.

4. Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume the number of litres sold follows the normal distribution with a standard deviation of 6 L. From his records, he selects a random sample of 12 sales and finds the mean number of litres sold is 38.

a. What is the point estimate of the population mean? (Round the final answer to the nearest whole number.)

The point estimate of the population mean is litres.

b. Develop a 95% confidence interval for the population mean. (Round the final answers to 3 decimal places.)

The 95% confidence interval for the population mean is between and .

c.Interpret the meaning of part (b).

If 100 such intervals were determined, the population (Click to select) variance mean would be included in about intervals.

5. A sample of 28 adults attending a country fair determined that the mean age was 38. Given that the population standard deviation is known to be 14, determine the 80 confidence interval for the population mean age. (Round the final answers to 3 decimal places.)

Confidence interval for the population mean is and .

6. A normal population has a mean of 82 and a standard deviation of 9. You select a sample of 55. Use Appendix B.1 for the z values.

Compute the probability that the sample mean is: (Round the z values to 2 decimal places and the finalanswers to 4 decimal places.)

a. Less than 81.

Probability

b. Between 81 and 83.

Probability

c. Between 83 and 86.

Probability

d. Greater than 86.

Probability

7.