HELP---statistics question!!!!!!!!!?

Question

I'm given a MEAN (83) and a STANDARD DEVIATION (10).

Then it asks where 95% of the distrubution is to fall?

The distrubution is mound-shaped.

How can I figure this out? I have 5 more problems like it and I can't get any of them. I've only been taught to get the 75%, 88.9%, and 93.5% distrubutions AND I've never been taught how to take the SHAPE of the distrubution into consideration.

I can't find the answers in the book. :-/

I also have to figure out the opposite of how to find the PERCENT if the shape is known and I have the numbers it falls between.

Any help is great.

THANK YOU SO MUCH!
You both rock! :)

Answer 1

Your "mound" shape is called a Normal or Bell probability distribution curve in most textbooks. Bell curves are the most common of all the distributions used in statistics, which is why they are also called the Normal curve.

As a consequence, most statisticians memorize some numbers about them. For example 95% of the area under a Bell curve lies in between the mean (m) and plus or minus two standard deviations (2z). In stat talk, we write P(x<= m+/-2z) = .95.

Thus, 95% of the area under the Bell curve (your mound) will come between LB = m - 2z and UB = m + 2z; where LB and UB are the lower and upper bounds between which 95% of the distribution's area lies. For your numbers LB = m - 2z = 83 - 2 X 10 = 63 and UB = 83 + 2 X 10 = 103.

In addition to P(x<= m+/-2z) = .95, we also memorize P(x<= m+/-3z) = .99 and P(x<= m+/-z) = .68 for Bell curves. These often come up in statistics.

I think you need to review your terminology. [See source.] A distribution is the shape of a frequency curve...of which the Bell curve is just one specific shape. A distribution is not some percentage, which you seem to think. The percentage (e.g., 75% and 88.9%) simply indicates how much area under the distribution curve is being considered, where 100% means all the area under the curve is being considered.

Answer 2

0.950 confidence is 1.96 standard deviations in mound shaped data. Thus, you should multiply 10 by 1.96 and get 19.6. You have 95% confidence that a piece of data would fall between 83 plus or minus 19.6.
Other pieces of data are given on the following page.

Answer 3

I don't have the answer but it has to do with a normal curve and Z- score. There should be a formula for that....its a pretty important statistic subject. I believe 1 Z is 98%, 2 Zs are 95%. Hope that points you in the right direction. Obviously its not that important in life if it hasn't stuck with me.