SOLUTION: Question: Could someone explain how to do this particular problem? What is the probability that a normal random variable has an outcome within 1 standard deviation of the mean?

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Question 919114: Question: Could someone explain how to do this particular problem?
What is the probability that a normal random variable has an outcome within 1 standard deviation of the mean?
Thanks for the help :)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
get a z-score table
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%7B%7B%7B%0D%0A%7B%7B%7Bsubtract the smaller area from the larger area
the result is your answer
as you can see in the table, z score of 1 gives an area to the left of it of .8413 and z score of -1 gives an area to the left of it of .1587
so, .8413+-+.1587+=+.6826
the probability will be 68.26%
that's the area under the normal distribution curve that's between a z score of -1 and a z score of 1
here is the picture of the area of a z score between -1 and 1 shown below:

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