The lives of Globewrite light bulbs made by Glowbuff Inc. have a mean of 1000 hours and standard deviation 160 hours. Assuming a normal distribution for the sample means, find the probability that 36 light bulbs will have a mean life of a. less than 940 hours? b. at least 1020 hours? c. in between 982 and 1030 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!
The lives of Globewrite light bulbs made by Glowbuff Inc. have a
a. less than 940 hours?
b. at least 1020 hours?
c. in between 982 and 1030 hours?
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