Extralite are testing a new long-life bulb. The lifetimes, in hours, are assumed to be normally dis- tributed with mean µ = 4650 and o = 400 (Round your answers to 4 decimal places): (a) Find the probability that a bulb chosen at random has a lifetime between 4250 and 4750 hours. (a) (b) Eztralite wish to quote a lifetime which will be exceeded by 99% of bulbs. What time, correct to the nearest 100 hours, should they quote? (b)
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!
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