S. A manufacturer of digital recorders claims the distribution of life of its recorders can be described by a normal distribution with a mean of 2500 hours and variance of 40000 hours. (15%) a. What is the probability that a randomly selected digital recorder lasts more than 2250 hours? b. If two digital recorders are randomly selected, what is the probability of neither lasting more than 2250 hours? c. If my digital recorder lasted longer than 28% of all the digital recorders, exactly how many hours was the life of my digital recorder? d. What is the sampling distribution of the sample mean of 64 random observations from this population? Find the probability of sample mean being between 2490 and 2518. e. Would your results in parts a - d remain valid if the life of digital recorders did not have a normal distribution? Explain.
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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