For each probability and percentile problem, draw the picture. The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. Part (f) Draw a graph of the probability distribution. Part (g) Find the probability that the person retired after age 69. (Round your answer to four decimal places.) Part (i) In a room of 1000 people over age 79, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.) people
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!
For each
The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.
Part (f)
Part (g)
Part (i)
people
The time (in years) after age 60 it takes an individual to retire is exponentially distributed with mean 6 years.
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