A random variable X has a normal distribution. (a) Describe two features of the distribution of X. A company produces electronic components which have life spans that are normally distributed. 1% of the components have a life span less than 3500 hours and 2.5% have a life span greater than 5500 hours. (b) Determine the mean and standard deviation of the life spans of the components. (c) If the company gives a warranty of 4000 hours on the components, find the proportion of components that the company can expect to replace under the warranty. (d) Tom purchased 20 electronic components. What is the probability that the mean life span of the 20 electronic components is less than 4500 hours?
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!
A random variable X has a normal distribution. (a) Describe two features of the distribution of X.
A company produces electronic components which have life spans that are
(b) Determine the mean and standard deviation of the life spans of the components.
(c) If the company gives a warranty of 4000 hours on the components, find the proportion of components that the company can expect to replace under the warranty.
(d) Tom purchased 20 electronic components. What is the probability that the mean life span of the 20 electronic components is less than 4500 hours?
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