Chapter 08, Section 8.2, Problem 020 Lazurus Steel Corporation produces iron rods that are supposed to be 33 inches long. The machine that makes these rods does not produce each rod exactly 33 inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is 33 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.3 inch. The quality control department takes a sample of 23 such rods every week, calculates the mean length of these rods, and makes a 97% confidence interval for the population mean. If either the upper limit of this confidence interval is greater than 33.05 inches or the lower limit of this confidence interval is less than 32.95 inches, the machine is stopped and adjusted. A recent sample of 23 rods produced a mean length of 33.05 inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such rods have a normal distribution. Round your answers to two decimal places. The confidence interval is to inches. The machine an adjustment. needs does not need Chapter 08, Section 8.2, Problem 022 A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 116 homeowners selected from this area showed that they pay an average of $1572 per month for their mortgages. The population standard deviation of such mortgages is $217. a. Find a 99% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. Round your answers to two decimal places. to dollars

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