Suppose a car driven under specific conditions gets a mean gas mileage of 40 miles per gallon with a standard deviation of 3 miles per gallon. On about what percentage of the trips will your gas mileage be above 43 miles per gallon? A) About 2.5%, because 43 miles per gallon is 2 std. deviations above the mean. By the 68-95-99.7 rule, about 2.5% of the distribution lies within 2 std. deviations of the mean. B) About 2.5%, because 43 miles per gallon is 2 std. deviations above the mean. By the 68-95-99.7 rule, about 95% of the distribution lies within 2 std. deviations of the mean. So 5% lies outside of this range, 2.5% in each tail. C) About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 1 std. deviation of the mean. So 32% lies outside of this range, 16% in each tail. D) About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 16% of the distribution lies within 1 std. deviation of the mean.
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!
Suppose a car driven under specific conditions gets a
C) About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 68% of the distribution lies within 1 std. deviation of the mean. So 32% lies outside of this range, 16% in each tail.
D) About 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the 68-95-99.7 rule, about 16% of the distribution lies within 1 std. deviation of the mean.
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