Question

When one thinks of the normal distribution, the first thing that comes to mind is the bell curve and grades. While this is one example of a normal curve that is widely recognized, it is not the only one. Come up with a unique normal distribution from literature that your classmates have not posted about already. Explain your normal curve with items such as the mean and standard deviation. What do the areas in the intervals µ - ? to µ + ?, µ - 2? to µ + 2? and µ - 3? to µ + 3? represent as far as areas under the normal curve? With the mean and standard deviation, calculate what the actual intervals are for your normal curve. Please include any citations regarding where you obtained the data for your curve.

Answer 1

SOLUTION:

The demonstration shows a graph of two normal distributions.

The red distribution has a standard deviation of 8 and mean of 30.

the blue distribution has a standard deviation of 20 and mean of 50

You can see that the blue distribution is more spread out than the red distribution.

The figure above is The 68-95-99.7 Rule For Normal Distributions

which states that

Approximately 68% of the observations fall within 1 standard deviation of the mean

Approximately 95% of the observations fall within 2 standard deviations of the mean

Approximately 99.7% of the observations fall within 3 standard deviations of the mean.

For Red distriibution:

mean =30

sd=8

For 68%

µ - ? =30-8=22

µ + ?=30+8=38

approximately 68% of the values lies in between 22 and 38

For95%:

µ - 2?=30-2(8)=30-16=14

µ + 2?=30+2(8)=30+16=46

Approximately 95% of values lies in between 14 and 46

For99.7% Rule:

µ - 3? =30-3(8)=30-24=6

µ + 3?=30+3(8)=30+24=54

Approximately 99.7% of values lies in between 6 and 54.

Calculate similarly for blue distribution.