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# Online Tutorial -CG50: Normal Distribution in Stats Mode

## Video Transcript

In this tutorial, we'll be looking at how to use the CG50 to calculate probabilities from boundaries and boundaries for probabilities for a general normal distribution. The questions where the mean and standard deviation of the distribution are known, there is now no need for coding. To work along with this tutorial, you may find it easiest to reset your calculator before starting so that your screen matches the one in the video.

The normal distribution can be found in stats mode, distribution and normal. F1 finds the probability that the random variable rounds to a particular integer value. F2 here finds the probability that the random variable lies in a given interval. If the interval you want is open like this one, choose an arbitrary very large boundary value. I'm going to use the interval 180 to a thousand.

Choose F2 and variable and input the boundary values, next the standard deviation and lastly the mean. The order here may catch you out. And then execute and the probability is given. Notice the z values for the boundaries are also given. A useful checking strategy is to view this in a graph, which illustrates the probability that you found. Exit and scroll down and press draw. Notice the graph is the standardised normal distribution, with the boundary values clearly marked.

Sometimes we know the distribution and the probability that the random variable falls in a given interval and the question then asks us to find the boundary value for this interval. Exit and choose distribution, normal and the inverse function, and set to variable. Choose the left tail, input the area - that's the probability value - input the standard deviation, the mean and execute. And now the boundary value is given. Notice in this case the boundary is negative, which would have been much more difficult to find using standard statistical tables. The same method can be used for more general normal distribution, without having to standardise. Press exit to go to the previous screen and scroll up to choose right tail. Input the area 0.35, the standard deviation of 15 and finally the mean of 100 and execute. So the boundary here has been found without any reference to the normal 0 1 distribution. Central regions found the boundary values, which are symmetric about the mean for a given area. The questions with an unknown mean or standard deviation, trial and improvement can be used with the techniques above and more traditional ways to use a coding method using the CG50 to find the boundary values from the 0 and 0 1 distribution.

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