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Hi there,

I would really appreciate some help with some concepts in stats that I am having trouble grasping. I cannot understand what is meant by 3 standard deviations from the mean. According to my Introductory Stats unit lecture notes, to get a 99.7% confidence interval, you add 3 standard deviations of the distribution to the mean of the distribution but the z-score corresponding to 99.7% is 2.78.

Thanks in advance

There could be three reasons for this.

1) It was a typo on somebody's part, since 3 standard deviations is not 99.7%, but has an 8 before the 7. It is really 99.87%. That is on the one sided test. If m is the average, s is the standard deviation, and x is some value, that says the P(x<=m+3s) = 0.9987.

2) It was a rounding error, since 3 standard deviations for a two sided test is 99.74%,

so the 4 was dropped in rounding to only one place past the decimal.

3) It was forgetting to put in the last digit, which is the same as the last one.

Most likely it is one of the above.

As an example, suppose we wanted to know the probability of being within (m-0.1s,m+0.1s).

Depending on which table is used (with 4, 3, or 2 places past the decimal), that would be

2*0.5398 = 1.0796, 2*0.540 = 1.080, 2*0.54 = 1.08. Note that mathematically, 1.08 is really 1.08±0.05, so it is between 1.075 and 1.085.

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