A Christmas tree light has an expected life of 210 hr and a standard deviation of 2 hr. (a) Find a bound on the probability that one of these Christmas tree lights will require replacement between 200 hr and 220 hr. (Enter your answer to two decimal places.)(b) Suppose a large city uses 160,000 of these Christmas tree lights as part of its Christmas decorations. Estimate the number of lights that are likely to require replacement between 190 hr and 230 hr of use.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A Christmas tree light has an expected life of 210 hr and a standard deviation of 2 hr.
(b) Suppose a large city uses 160,000 of these Christmas tree lights as part of its Christmas decorations. Estimate the number of lights that are likely to require replacement between 190 hr and 230 hr of use.
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