SOLUTION: Hello Could someone give me a hand with the following: What is the probability that a normal random variable has an outcome within 1 standard deviation of the mean? thank

Question 888693: Hello
Could someone give me a hand with the following:
What is the probability that a normal random variable has an outcome within 1 standard deviation of the mean?
thanks
Paul
Found 3 solutions by Theo, rothauserc, oscargut:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the probability will be approximately 68%.
.6826894809 to be more exact, taken from my TI-84 Plus Calculator.

if you want to calculate it from the z-score table, you would do the following:

get a z-score table like the following one.

http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

look up the area to the left of a z score of 1
look up the area to the left of a z score of -1
subtract the smaller area from the larger area.
the result is your answer.

in this table...
z score of 1 gives an area to the left of it of .8413
z score of -1 gives an area to the left of it of .1587

.8413 - .1587 = .6826

that's the area under the normal distribution curve that's between a z score of -1 and a z score of 1.

there's an online z score calculator that will show you this in pictures.

that calculator can be found at the following link:

http://davidmlane.com/hyperstat/z_table.html

the picture of the area of a z score between -1 and 1 is shown below:

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
68% of values are within 1 standard deviation of the mean
therefore,
the probability that a normal random variable has an outcome within 1 standard deviation of the mean is 68%.

Answer by oscargut(2103)   (Show Source): You can put this solution on YOUR website!
Hi
You must compute P(-1 You can ask me more at:
mthman@gmail.com
Thanks
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