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1. The mean inside diameter of a washer produced by a machine is 0.502 inches and the standard deviation is 0.005 inches. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inches, otherwise the washers are considered defective. Assuming the diameters are normally distributed, find: a. The probability that the inside diameter of a randomly chosen washer is less than 0.515 inches b. The probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches

2. A large population is normally distributed with a standard deviation of 0.12. A random sample will be taken from this population and the sample mean will be calculated. We require at least 98% confidence that the true population mean will be within 0.05 of the sample mean, assuming there is no systematic error. What sample size is required? Hint: Recall the general form of a confidence interval