# Question

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 Questions

Let 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 ...Post your question

0