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The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.85 pounds with a standard deviation of 1.02pounds. In a recent study, a group of 45people who used this pill were interviewed. The study revealed that these people lost a mean of 1.68 pounds after one week. If the producer’s claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.68 pounds or more?
A machine that manufactures automobile pistons is estimated to produce a defective piston 1% of the time. Suppose that this estimate is correct and that a random sample of 80 pistons produced by this machine is taken. Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.