In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is estimated that 3.6% of the general population will live past their 90th birthday. In a graduating class of 758 high school seniors, find the following probabilities. (Round your answers to four decimal places.) (a) 15 or more will live beyond their 90th birthday (b) 30 or more will live beyond their 90th birthday (c) between 25 and 35 will live beyond their 90th birthday (d) more than 40 will live beyond their 90th birthday
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!
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the
It is estimated that 3.6% of the general population will live past their 90th birthday. In a graduating class of 758 high school seniors, find the following probabilities. (Round your answers to four decimal places.)
(b) 30 or more will live beyond their 90th birthday
(c) between 25 and 35 will live beyond their 90th birthday
(d) more than 40 will live beyond their 90th birthday
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