Question

2. In a set of 400 values, the mean is 121 and the standard deviation is 14. Estimate how many values fall in between each interval

a) 107 – 135=

b)93 - 149=

c) 79 - 163=

Answer 1

Normal distribution?

Answer 2

yes standard deviation

Answer 3

If this is normal, then 68.4% of values fall in between plus/minus sigma (within two sigmas), 95.4% - within plus/minus two sigmas (within four sigmas) and 99.6% - within six sigmas.

Answer 4

a)

Both 107 and 135 are 1 standard deviation away from the mean. So by the empirical rule, about 68% of the distribution is in this interval.

So 68% of 400 is 0.68*400 = 272

which means that there are roughly 272 values in this interval.

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b)

Here 95% of the distribution lives because we're now 2 standard deviations away from the mean.


So 0.95*400 = 380 values are in this range


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c)

We're now 3 standard deviations away from the mean. So 99.7% of the values are found here.

0.997 * 400 = 398.8


So roughly 399 values are found here.

Answer 5

http://en.wikipedia.org/wiki/Normal_distribution note distribution histogram on the page