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(5) Suppose that a large conference room at a certain company can be reserved for no more than 4 hours. Both long and short conferences occur quite often. In fact,it can be assumed that the length X of a conference has a uniform distribution on the interval [0, 4]. (i) What is the probability density function? (ii) What is the probability that any given conference lasts at least 3 hours? (6) In an industrial process, the diameter of a ball bearing is an important measurement. The buyer sets specifications for the diameter to be 3.00.01 cm. The implication is that no part falling outside these specifications will be accepted. It is known that in the process the diameter of a ball bearing has a normal distribution with mean μ = 3.0 and standard deviation σ = 0.005. On average, how many manufactured ball bearings will be scrapped?
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