A certain manufacturer makes 400w light bulbs. Assume that these light bulbs have lifetimes that are normally distributed with a mean lifetime of 410 hours and a standard deviation of 52 hours. Use this table or the ALEKS calculator to find the percentage of light bulbs with lifetimes shorter than 371 hours. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).
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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