3.1. A manufacturing company regularly conducts quality control checks at specified periods on all products manufactured by the company. A new order for 2000 light bulbs is due to be delivered to a large franchise hardware store. Historically, the manufacturing record has a failure rate of 15% and the sample to be tested consists of four randomly selected light bulbs that are drawn from the delivery consignment. From this information estimate the following probabilities. 3.1.1. Find the probability distribution for 0, 1, 2, 3 and 4 defective light bulbs in the sample of four drawn. 3.1.2. Calculate the probability that at least 3 will be defective. 3.1.3. Determine the mean and variance f the distribution.

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