Births The probability of a baby being born a boy is 0.512. Consider the problem of finding the probability of exactly 7 boys in 11 births. Solve that problem using (1) normal approximation to the binomial using Table A-2; (2) normal approximation to the binomial using technology instead of Table A-2; (3) using technology with the binomial distribution instead of using a normal approximation. Compare the results. Given that the requirements for using the normal approximation are just barely met, are the approximations off by very much?
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!
Births The probability of a baby being born a boy is 0.512. Consider the problem of finding the probability of exactly 7 boys in 11 births. Solve that problem using (1) normal approximation to the binomial using Table A-2; (2) normal approximation to the binomial using technology instead of Table A-2; (3) using technology with the binomial distribution instead of using a normal approximation. Compare the results. Given that the requirements for using the normal approximation are just barely met, are the approximations off by very much?
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