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# Online Tutorial - CG50: Binomial Distribution in Stats Mode

## Video Transcript

In this tutorial, we're looking at calculating probabilities using the binomial distribution. We also look how the CG50 can find a critical region for a hypothesis test, based on the binomial distribution. You may find it easiest to reset your calculator before starting so the screen matches the one in the video.

The binomial distribution is found in stats mode. Distributions and binomial use F1 for Bpd. This finds the probability of a single value. Set the data to variable, input the seven for x, 10 for the number of trials and 0.6 for the probability. Execute gives the answer then to eight decimal places. Press exit and go back through the menus ready for the next calculation.

Choose distribution and binomial as before, but now use Bcd and variable. Scroll down to input to the smallest and the largest values of X. Do take care if your region has a strict inequality. There's no need to retype the values for N and P. Just execute.

If you're doing a hypothesis test based on the binomial distribution, you'll probably want to find the critical regions. You may want to use the inverse probability function. Exit the cumulative menu, back as far as choosing distribution, binomial and inverse. Scroll down to choose a 5% area for the bottom tail of the distribution and enter 0.05. Put 50 and 0.05 as the new values on N and P, and execute. The value x equals 19 is closest to be 5% but it may be over 5%. We need to check the cumulative probabilities, to find consecutive values for which the cumulative probabilities go from under 5% to over 5%. Go back through the menus and choose cumulative probabilities. Calculate and then record the probability that x is less than or equal to 19.

Repeat this for 18 and notice this is on the other side of 5%. Remember to record both of these probabilities as evidence that your critical region is the correct one. For the critical region at the top end, go back through the menus and choose distribution, binomial and inverse menu. Choose 95% for the area, so that the top tail has a probability of 5%. The warning shows that had the area only been 0.01 different, X equals 30 would have been the value, instead of 31. Exit to remove the warning and then go back through the menus to check the cumulative probabilities of at least 31. There's no need to change N and P. And notice this is more than 5%, so go back and check the critical region starting with 32. This is less than 5%, so these two answers together are evidence that the critical region starts at 32.

Remember to give both tails and all the supporting evidence in your written answer. You can find a handout showing how to display a table of all the cumulative probabilities, as well as many other resources at education.casio.co.uk.