800 700 600 500 400 300 200 100 10 20 30 40 50 60 70 80 or a certain state, the function f(x) = 0.4x2 – 36x + 990 hodels the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, where x includes drivers from ages 16 to 74, inclusive. The raph of f is shown above. Use the equation for f to solve: Find the number of accidents per 50 million miles driven for drivers age 19. nswer: accidents per 50 million miles ) Find the number of accidents per 50 million miles driven for drivers age 35. nswer: accidents per 50 million miles For what value of x does the graph have its lowest point? This is the age of drivers with the fewest accidents. nswer:
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!
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