3.7 Normal Approximation to the Binomial Distribution

Normal Approximation to the Binomial Distribution

  • Binomial distributions depend on n and p. We will observe that as n increases, if we plot the probability distribution of the binomial distribution, a ‘bell curve’ which is a symbolic shape of normal distribution, emerges. Below is the plot of the binomal distribution for n=10,\ 20,\ 50,\ 100 and p=0.2,\ 0.5,\ 0.8.
  • As you can see, as n increases, a smoother bell curve is seen. As for p, it only decides if the curve is slanted (or specifically ‘skewed’) to the left or right.
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3.6 Real-Life Application of Normal Distributions

Applying Normal Distributions in Real Life

  • Normal distribution is used to model many things in real life as it is a very reasonable model. Therefore, knowing how to apply the knowledge of normal distributions in real life problems is important.

Example

The time taken to complete a logical reasoning task is normally distributed with a mean of 55 seconds and a standard deviation of 8 seconds. Keeping the answer as accurate to 4 d.p.,

a) Find the probability that that a randomly chosen person will take less than 50 seconds to complete the task.

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