10. To become an actuary, it is necessary to pass a series of exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program. The mean score of the sample is 6.0, and the standard deviation of the sample is 2.0. We do not know the standard deviation of the population.

Referring to Scenario 2, any confidence interval calculation will be based on __________ degrees of freedom.

11.

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. It is known that the standard deviation in the cutting length that this machine produces is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a confidence interval for the mean length cut by machine.

Referring to Scenario 1, the Z value to use in obtaining the 99% confidence interval is approximately ________.