1. The administrator of a physical therapy facility has found that postoperative performance scores on a knee flexibility test have tended to follow a normal distribution with a standard deviation of 4. For a simple random sample of ten patients who have recently had knee surgery, the scores are as follows: 101, 92, 94, 88, 52, 93, 76, 84, 72, and 98. Construct and interpret the 90% and 95% confidence intervals for the population mean.

2. In testing the heat resistance of electrical compo- nents, safety engineers for an appliance manufacturer routinely subject wiring connectors to a temperature of 450 degrees Fahrenheit, then record the amount of time it takes for the connector to melt and cause a   short circuit. Past experience has shown the standard deviation of failure times to be 6.4 seconds. In a simple random sample of 40 connectors from a very large  production run, the mean time until failure was found to be 35.5 seconds. Construct and interpret the 99% confi- dence interval for µ 5 the mean time until failure for all of the connectors from the production run.