The lifetimes of light bulbs are normally distributed with a mean of 1520 hours and a standard deviation of 180 hours. -Determine the proportion of light bulbs lasting less than 1360 hours. Round your answer to 4 decimal places. -The longest lasting 20 percent of light bulbs last _____ hours or more. Round your answer to 1 decimal place. -The middle 80 percent of light bulbs last between _____ and _____ hours. Round your answers to 1 decimal place. -Determine the proportion of light bulbs lasting between 1400 and 1700 hours. Round your answer to 4 decimal places. -Determine the proportion of light bulbs lasting more than 1640 hours. Round your answer to 4 decimal places. -The shortest-lasting 10 percent of light bulbs last _____ hours or less. Round your answer to 1 decimal place.
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!
The lifetimes of light bulbs are
-Determine the proportion of light bulbs lasting less than 1360 hours. Round your answer to 4 decimal places.
-The longest lasting 20 percent of light bulbs last _____ hours or more. Round your answer to 1 decimal place.
-The middle 80 percent of light bulbs last between _____ and _____ hours. Round your answers to 1 decimal place.
-Determine the proportion of light bulbs lasting between 1400 and 1700 hours. Round your answer to 4 decimal places.
-Determine the proportion of light bulbs lasting more than 1640 hours. Round your answer to 4 decimal places.
-The shortest-lasting 10 percent of light bulbs last _____ hours or less. Round your answer to 1 decimal place.
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