# Question

Let X be the number of defective items found by a quality inspector in a random batch of 15 items from a particular manufacturing process. The probability distribution of X is provided in the file S04_18.xlsx. This firm earns $500 profit from the sale of each acceptable item in a given batch. In the event that an item is found to be defective, it must be reworked at a cost of $100 before it can be sold, thus reducing its per-unit profit to $400.

a. Find the mean and standard deviation of the profit earned from the sale of all items in a given batch.

b. What is the probability that the profit earned from the sale of all items in a given batch is within two standard deviations of the mean profit level? Is this result consistent with the empirical rules from Chapter 2? Explain.

a. Find the mean and standard deviation of the profit earned from the sale of all items in a given batch.

b. What is the probability that the profit earned from the sale of all items in a given batch is within two standard deviations of the mean profit level? Is this result consistent with the empirical rules from Chapter 2? Explain.

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