The following table shows the approximate numbers of school goers in the United States (residents who attended some educational institution) in 1998, broken down by age group. Age 3−6.9 7−12.9 13−16.9 17−22.9 23−26.9 27−42.9 Population (millions) 9 20 15 13 3 5 Use the rounded midpoints of the given measurement classes to compute the probability P distribution of the age X of a school goer. (Round probabilities to four decimal places.) Age 5 10 15 20 25 35 P(X = x) Compute the expected value of X, E(X). (Round your answer to one decimal place.) E(X) =
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 following table shows the approximate numbers of school goers in the United States (residents who attended some educational institution) in 1998, broken down by age group.
| Age | 3−6.9 | 7−12.9 | 13−16.9 | 17−22.9 | 23−26.9 | 27−42.9 |
| Population (millions) |
9 | 20 | 15 | 13 | 3 | 5 |
Use the rounded midpoints of the given measurement classes to compute the
| Age | 5 | 10 | 15 | 20 | 25 | 35 |
| P(X = x) |
Compute the
E(X) =
What information does the expected value give about residents enrolled in schools? (Round your answer to one decimal place.)
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