The number of fatalities due to car crashes, based on the number of miles driven, begins to climb after the driver is past age 65. Aside from declining ability as one ages, the older driver is more fragile. The number of fatalities per 100 million vehicle miles driven is approximately N(x) = 0.0336x3 − 0.118x2 + 0.215x + 0.7 (0 ≤ x ≤ 7) where x denotes the age group of drivers, with x = 0 corresponding to those aged 50–54, x = 1 corresponding to those aged 55–59, x = 2 corresponding to those aged 60–64, …, and x = 7 corresponding to those aged 85–89.† What is the fatality rate per 100 million vehicle miles driven for an average driver in the 50–54 age group? In the 75–79 age group?
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!
Aging Drivers
The number of fatalities due to car crashes, based on the number of miles driven, begins to climb after the driver is past age 65. Aside from declining ability as one ages, the older driver is more fragile. The number of fatalities per 100 million vehicle miles driven is approximately
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