Suppose that we want to use the normal approxi-mation to the binomial distribution to determine b(1; 150, 0.05).(a) Based on the rule of thumb in Section 6, would we bejustified in using the approximation?(b) Make the approximation and round to four decimals.(c) If a computer printout shows that b(1; 150, 0.05) =0.0036 rounded to four decimals, what is the percentageerror of the approximation obtained in part (b)?This serves to illustrate that the rule of thumb is justthat and no more; making approximations like this alsorequires a good deal of professional judgment.
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!
mation to the binomial distribution to determine b(1;
(a) Based on the rule of thumb in Section 6, would we be
justified in using the approximation?
(b) Make the approximation and round to four decimals.(c) If a computer printout shows that b(1; 150, 0.05) =
0.0036 rounded to four decimals, what is the percentage
error of the approximation obtained in part (b)?
This serves to illustrate that the rule of thumb is just
that and no more; making approximations like this also
requires a good deal of professional judgment.
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