Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 6.4 years and a standard deviation of 1.8 years. Find the probability that a randomly selected DVD player will have a replacement time less than 1.7 years? P(X < 1.7 years) = Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or Z-Scores rounded to 3 decimal places are accepted. If the company wants to provide a warranty so that only 3.7% of the DVD players will be replaced before the warranty expires, what is the time length of the warranty? warranty = years Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
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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