According to actuarial tables, life spans in the United States are approximately normally distributed with a mean of about 75 years and a standard deviation of about 16 years. By computing the areas under the associated normal curve, find the following probabilities. Source: Psychological Science. (a) Find the probability that a randomly selected person lives less than 88 years (b) Find the probability that a randomly selected person lives more than 67 years. (c) Find the probability that a randomly selected person lives between 61 and 70 years.
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!
According to actuarial tables, life spans in the United States are approximately
distributed
computing the areas under the associated normal curve, find the following probabilities.
Source: Psychological Science.
(a) Find the
(b) Find the probability that a randomly selected person lives more than 67 years.
(c) Find the probability that a randomly selected person lives between 61 and 70 years.
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