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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 243.1-cm and a standard deviation of 1.9-cm. For shipment, 47 steel rods are bundled together. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - NO b. What is the distribution of ? ~ N( c. For a single randomly selected steel rod, find the probability that the length is between 243.2-cm and 243.4-cm. d. For a bundled of 47 rods, find the probability that the average length is between 243.2-cm and 243.4-cm. e. For part d), is the assumption of normal necessary? Yes No
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 25 weeks. Assume that the length of unemployment is normally distributed with population mean of 25 weeks and the population standard deviation of 3 weeks. Suppose you would like to select a random sample of 9 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places. a. What is the distribution of X? X - N( b. What is the distribution of ? ~ N( c. What is the probability that one randomly selected individual found the next job is less than 24 weeks? d. For 9 unemployed individuals, find the probability that the average time that they found the next job is less than 24 weeks. e. For part d), is the assumption of normal necessary? O No Yes