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# ACMMM168

## 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.
Read More »3.7 Normal Approximation to the Binomial Distribution ## 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.

Read More »3.6 Real-Life Application of Normal Distributions