The first distribution pictured above has a smaller standard deviation, and so more of the data are heavily concentrated around the mean than in the second distribution. Also, in the first distribution, there are fewer data values at the extremes than in the second distribution. Because the second distribution has a larger standard deviation, the data are spread farther from the mean value, with more of the data appearing in the tails. Technology Note: Investigating the Normal Distribution on a TI-83/84 Graphing Calculator We can graph a normal curve for a probability distribution on the TI-83/84 calculator. To do so, first press [Y=] . To create a normal distribution, we will draw an idealized curve using something called a density function. The command is called 'normalpdf(', and it is found by pressing [2nd][DISTR][1] . Enter an X to represent the random variable, followed by the mean and the standard deviation, all separated by commas. For this example, choose a mean of 5 and a standard deviation of 1. Adjust your window to match the following settings and press [GRAPH] . Press [2ND][QUIT] to go to the home screen. We can draw a vertical line at the mean to show it is in the center of the distribution by pressing [2ND][DRAW]and choosing 'Vertical'. Enter the mean, which is 5, and press [ENTER] . Remember that even though the graph appears to touch the -axis, it is actually just very close to it. In your Y= Menu, enter the following to graph 3 different normal distributions, each with a different standard deviation: This makes it easy to see the change in spread when the standard deviation changes.
The first distribution pictured above has a smaller standard deviation, and so more of the data are heavily concentrated around the mean than in the second distribution. Also, in the first distribution, there are fewer data values at the extremes than in the second distribution. Because the second distribution has a larger standard deviation, the data are spread farther from the mean value, with more of the data appearing in the tails. Technology Note: Investigating the Normal Distribution on a TI-83/84 Graphing Calculator We can graph a normal curve for a probability distribution on the TI-83/84 calculator. To do so, first press [Y=] . To create a normal distribution, we will draw an idealized curve using something called a density function. The command is called 'normalpdf(', and it is found by pressing [2nd][DISTR][1] . Enter an X to represent the random variable, followed by the mean and the standard deviation, all separated by commas. For this example, choose a mean of 5 and a standard deviation of 1. Adjust your window to match the following settings and press [GRAPH] . Press [2ND][QUIT] to go to the home screen. We can draw a vertical line at the mean to show it is in the center of the distribution by pressing [2ND][DRAW]and choosing 'Vertical'. Enter the mean, which is 5, and press [ENTER] . Remember that even though the graph appears to touch the -axis, it is actually just very close to it. In your Y= Menu, enter the following to graph 3 different normal distributions, each with a different standard deviation: This makes it easy to see the change in spread when the standard deviation changes.
normal_distribution_-_determining_the_number_of_std._deviations_form_mean.docx