3. If the Manufacturer knows the probability of a manufactured device being defective is 0.30 and she is to manufacture 4 devices, finish the following table provided that X is the number of defective devices [10 Marks] | x | 0 | 1 | 2 | 3 | 4 | | :---: | :---: | :---: | :---: | :---: | :---: | | P(x) | 0.24 | | | | | a) What is the probability that at most 2 of the manufactured devices will be defective? b) What is the probability that at least 2 of the manufactured devices will be defective? c) What is the probability that the number of defective devices will be between 1 and 4? d) Calculate E(X) and V(X) using the table and then using the binomial distribution. Compare the results.
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We can use the binomial probability formula for this: P(X = x) = C(n, x) * p^x * (1-p)^(n-x) where C(n, x) is the number of combinations of n items taken x at a time, p is the probability of a device being defective (0.30), and n is the total number of devices Show more…
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