# How to find probability?



## valley_girl1919 (Jun 18, 2007)

Ga my statistics class is killing me does anyone know how to do this? 

A random variable is normally distributed with a mean of = 50 and a standard deviation of = 5.

What is the probability the random variable will assume a value between 40 and 60 (to 4 decimals)?

What are the steps to find this?


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## Wirt (Jan 16, 2009)

I think there's a few ways to figure it out

the main way is with the..uh...empirical rule (had to look that up again,lol)

but one St. dev is 68% of the population, 2 std. dev's is 95%, and 3 std. dev's is 99.7%

so you're looking for 2 standard deviations away from the mean (50-5-5=40 and 50+5+5=60). So it'd be 95% probability

Not sure if there's a more mathematical way to go about it if someone else has another way (the 'to four decimal places' kinda throws me off)

(sorry, i had the percentages mixed up so i edited)
(sorry for all the parentheses )


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## Ambivert (Jan 16, 2010)

I think its this...

you find the z-scores for 60 and 40 and since its normal distribution it makes your life easier

z(60)=60-50/5=2
z(40)=40-50/5=-2

you need a z-score to probability calculator or chart (google them) and...

p(60)=97.725
p(40)=2.275
subtract from each other (taking one probability area under the curve and subtracting by the other probability area to find the area between) and voila!!... 

answer: 95.45%


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## Wirt (Jan 16, 2009)

ah yea, thats right


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## valley_girl1919 (Jun 18, 2007)

thanks for the help


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