Company XYZ knows that replacement times for the coffee makers it produces are normally distributed with a mean of 7.5 years and a standard deviation of 1.3 years. Let X be the replacement time of a randomly selected coffee maker. Please show the following answers to 4 decimal places. If a coffee maker is randomly chosen, find the probability that it will be replaced in at most 4.5 years. If a coffee maker is randomly chosen, find the probability that it will be replaced between 4.8 and 7.3 years. Please show the following answer to 1 decimal place. If the company wants to provide a warranty so that only 8% of the coffee makers will be replaced before the warranty expires, what is the time length of the warranty?
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!
Company XYZ knows that replacement times for the coffee makers it produces are
Please show the following answers to 4 decimal places.
- If a coffee maker is randomly chosen, find the
probability that it will be replaced in at most 4.5 years. - If a coffee maker is randomly chosen, find the probability that it will be replaced between 4.8 and 7.3 years.
Please show the following answer to 1 decimal place.
- If the company wants to provide a warranty so that only 8% of the coffee makers will be replaced before the warranty expires, what is the time length of the warranty?
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