The lifetime of a lightbulb in a certain application is normally distributed with mean μ = 1400 hours and standard deviation σ = 200 hours. a) What is the probability that a lightbulb will last more than 1800 hours? b) Find the 10th percentile of the lifetimes. c) A particular lightbulb lasts 1645 hours. What percentile is its lifetime on? d) What is the probability that the lifetime of a light-bulb is between 1350 and 1550 hours? e) Eight lightbulbs are chosen at random. What is the probability that exactly two of them have lifetimes between 1350 and 1550 hours?
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!
The lifetime of a lightbulb in a certain application is
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