A consumer buys n light bulbs, each of which has a lifetime that has a mean of 800 hours, a standard deviation of 100 hours, and a normal distribution. A light bulb is replaced by another as soon as it turns out. Assuming independence of the lifetimes, find the smallest n so that the succession of light bulbs produces light for at least 10,000 hours with a probability of 0.90.
Answer to relevant QuestionsLet the independent random variables X1 and X2 be N(0,1) and χ2(r), respectively. Let Y1 = X1/√X2/r and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and show that Y1 has a t ...At a heat-treating company, iron castings and steel forgings are heat-treated to achieve desired mechanical properties and machinability. One steel forging is annealed to soften the part for each machining. Two lots of this ...A random sample of size n = 18 is taken from the distribution with pdf f(x) = 1 − x/2, 0 ≤ x ≤ 2. (a) Find μ and σ2. (b) Find P(2/3 ≤ X ≤ 5/6), approximately. Let X equal the number out of n = 48 mature aster seeds that will germinate when p = 0.75 is the probability that a particular seed germinates. Approximate P(35 ≤ X ≤ 40). Ledolter and Hogg report that a manufacturer of metal alloys is concerned about customer complaints regarding the lack of uniformity in the melting points of one of the firm’s alloy filaments. Fifty filaments are selected ...
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