Draw 100 random samples from a binomial distribution with parameters n = 20 and p = .4. Consider an approximation to this distribution by a normal distribution with mean = np = 4 and variance = npq = 2.4. Draw 100 random samples from the normal approximation. Plot the two frequency distributions on the same graph, and compare the results. Do you think the normal approximation is adequate here?
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!
Draw 100 random samples from a binomial distribution
with parameters n = 20 and p = .4. Consider an approximation to this distribution by a
np = 4 and variance = npq = 2.4. Draw 100 random samples
from the normal approximation. Plot the two frequency distributions on the same graph, and compare the results. Do you
think the normal approximation is adequate here?
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