Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 137 pages if the mean is 191 pages and the standard deviation is 27 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
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!
Lisa has collected data to find that the number of pages per book on a book shelf has a
Solution:
Let X be the number of pages per book on a book shelf.
From the given information, X follows normal distribution with mean µ=191 pages and a standard deviation σ=27 pages.
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