Suppose 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is (a) At most 30? (b) Less than 30? (c) Between 15 and 25 (inclusive)?
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1. We can approximate this binomial distribution with a normal distribution since n is large. The mean and variance of the binomial distribution are: Mean: μ = np = 200 * 0.1 = 20 Variance: σ^2 = np(1-p) = 200 * 0.1 * 0.9 = 18 Now, we can use the normal Show more…
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Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let Xdenote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) (a) What is the (approximate) probability that X is at most 30? (b) What is the (approximate) probability that X is less than 30? (c) What is the (approximate) probability that X is between 15 and 25 (inclusive)?
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Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is a. At most 30? b. Less than 30? c. Between 15 and 25 (inclusive)?
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