Breckie Electrics makes electric shavers. The life x of an electric shaver manufactured by this corporation has a normal distribution with a mean of 70 months and a standard deviation of 6 months. The company is to determine the warranty period for this shaver. Any shaver that needs a major repair during this warranty period will be replaced free by the company. (a) What should the warranty period be if the company does not want to replace more than 6% of the shavers? (b) Find x such that 75% of shavers life is less than x? (c) What percentage of shavers do not need major servicing before 90 months?
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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