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ASSIGNMENT 5 2 2 2 1. Find the centroid of the p solid bounded above by the sphere x + y + z = 4 2 2 and below by the cone z = x + y . 2. A fair die is rolled repeatedly five times. What is the probability that 1 turns up exactly three times? What is the probability that 1 turns up at least three times? 3. If the probability of producing a defective lightbulb is p = 0.005, what is the probability that o lot of 2000 lightbulbs will contain more than six defectives? 4. If the lifetime X of a certain kind of automobile battery is normally distributed with mean of 4 yr and a variance of 1 yr, and the manufacturer wishes to guarantee the battery for 3 yr, what percentage of the batteries is he expected to replace under the guarantee? 5. Let X be a random variable with binomial distribution B(n; p). What is the probability that X takes an even value? Hint. Use the binomial formula (a + b)n = nk ak bn−k to express (p + q)n and (p − q)n , where q = 1 − p. 1