MHB Empirical rule calculator command

[aprilryan]

I just had a quick question. One problem says, "about 68% of the data will fall between what values?" Will I use the binompdf or normalcdf command on the TI-83 calculator? I can't remember.

Thanks!

 

[MarkFL]

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations.
• 99.7% fall within three standard deviations.

The rule is also called the 68-95-99 7 Rule or the Three Sigma Rule.

When applying the Empirical Rule to a data set the following conditions are true:

• Approximately 68% of the data falls within one standard deviation of the mean (or between the mean – one times the standard deviation, and the mean + 1 times the standard deviation). In mathematical notation, this is represented as: $\mu\pm\sigma$
• Approximately 95% of the data falls within two standard deviations of the mean (or between the mean – 2 times the standard deviation, and the mean + 2 times the standard deviation). The mathematical notation for this is: $\mu\pm2\sigma$
• Approximately 99.7% of the data falls within three standard deviations of the mean (or between the mean – three times the standard deviation and the mean + three times the standard deviation). The following notation is used to represent this fact: $\mu\pm3\sigma$

 

[aprilryan]

Basically I subtract the mean 95-2 and also add 95+2 to get between 75 and 112 right? It's much clearer now thanks! Love the profile pic by the way!

 

[MarkFL]

Basically I subtract the mean 95-2 and also add 95+2 to get between 75 and 112 right? It's much clearer now thanks! Love the profile pic by the way!

If you know the mean and the standard deviation, then the empirical rule can be used to say how much of the data will fall within certain ranges. For example, human IQ scores (which are normally distributed) have a mean of 100 and a standard deviation of 15. Using the empirical rule, we can then say:

• 68% of IQ scores are in the range 85-115. (100 ± 1·15)
• 95% of IQ scores are in the range 70-130. (100 ± 2·15)
• 99.7% of IQ scores are in the range 55-145. (100 ± 3·15)

Oh, and yes...I've been an avid fan of Rush since I was in elementary school...got my first album in 1976. (Rock)

 

[aprilryan]

I haven't listened to Rush in a long time. Will give them a listen! A math helper who likes Rush is always a plus! Thanks again!