The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months. Assume that the lives of dishwashers are normally distributed. a. What is the probability that a randomly selected dishwasher will have a life expectancy of at least 7 years? b. Dishwashers that fail operating in less than 4 years will be replaced free of charge. What percent of dishwashers are expected to be replaced free of charge? c. What are the minimum and the maximum life expectancy of the middle 95% of the dishwashers' lives? Give your answer in 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!
The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months. Assume that the lives of dishwashers are normally distributed.
a.
What is the probability that a randomly selected dishwasher will have a life expectancy of at least 7 years?
b.
Dishwashers that fail operating in less than 4 years will be replaced free of charge. What percent of dishwashers are expected to be replaced free of charge?
c.
What are the minimum and the maximum life expectancy of the middle 95% of the dishwashers' lives? Give your answer in months.
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