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
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Probability-and-statistics
-> 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
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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:
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:
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%.
