Normal Distribtion

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Normal Distribtion
Message posted by Amy Pennington on September 24, 1999 at 12:00 AM (ET)

I have several questions concerning Normal Distribution:

1. Is normal distribution the same as standard normal distribution? If not what are the differences

2. Is the reason that you convert the z-score to a percent using the statistical tables to determine a percentage or percentile?

3. I don't understand when you and 50% or subtract 50 from a converted z-score. I don't understand the concept.

Thanks for your help

Amy

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Normal Distribtion
Message posted by JG on September 24, 1999 at 12:00 AM (ET)

1 Z = (N-mean)/(S.D.)

2 Usually we work with percentiles

3 P(Z>1.0) = 0.159 ,
P(0

Re: Normal Distribtion
Message posted by JG on September 24, 1999 at 12:00 AM (ET)

3 P(Z<1.0) = .5 + .341 = 1-.159, etc.

Re: Normal Distribtion
Message posted by Joe Erdeky on September 25, 1999 at 12:00 AM (ET)

1 No. A normal distribution may have any mean and SD. The SND has mean = 0 and SD = 1.

3 If a positive z-score gives table value B,
.5+B= the area to the left of z.
.5-B= the area to the right of z.

Re: Normal Distribtion
Message posted by Amy Pennington on September 25, 1999 at 12:00 AM (ET)

Thanks for your responses, but I was not interested in formulas, but concepts or theory. I don't understand the
concepts and I need help.

Thanks

Amy

Re: Normal Distribtion
Message posted by Phil Rosenkrantz on September 25, 1999 at 12:00 AM (ET)

1. The standard normal distribution is just one normal distribution out of the infinite many you could have. After all, you can have a normal distribution with any combination of average (mean) and standard deviation you want (it is the shape that makes it normal...the "bell shape", if you will). However, the standard normal is a special one. The average is at zero and the standard deviation is 1.

It would be hard to have a table for every possible standard deviation. But we can convert (or "transform") every normal distribution into the standard normal using the z-transformation: z = (x-mean)/(std.dev.). Then we only need one table, the standard normal.

2. The table tells you the probability of being at or below any particular value of z (or x). If you multiply by 100, then you have a percentage (or percentile, if you use the word properly).

A brief example. Say the average age of college women is 24 years old with a standard deviation of 4 years. If you want to find the PROBABILITY that a college woman is under age 22, then you convert 22 to a z value and look up the probability (around .157). That means that 15.7 percent of college women are at or under age 22. You could also say that the 16th percentile is about age 22 if you wanted to.Note: Mathematicians, statisticians, and engineers like to talk in terms of "probabilities". Business and social science majors like to talk in terms of "percentage". You will often see this reflected in the background of your instructor. The calculations are the same, the difference is just in how you express the final answer.

3. Regarding the stupid standard normal table that cuts the distribution in half. Get rid of it if you can and copy one from a book that gives you the z-values that start at -3.4 and go all the way up to +3.4. I give copies to my students.

Hope that helps a little.

Re: Normal Distribtion
Message posted by Phil Rosenkrantz on September 25, 1999 at 12:00 AM (ET)

Oops. In my previous post, the standard deviation I used in my example should have been 2, not 4. That give a z value of -1.

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