How to solve this problem about averages and standard deviations?
2015-10-25 9:59 pm
A set of measurements of a parameter x has a normal distribution with mean of 50 and standard deviation of 1. If there are a very large number of measurements, approximately what percentage of measurements would you expect to lie OUTSIDE of 47 < x < 53 (i.e. not be in the range from 47 to 53)?
回答 (1)
2015-10-26 10:12 am
✔ 最佳答案
P( x > 53 )= P( Z > (53-50)/1 ) , where Z ~ N(0,1)
= P( Z > 3 )
= 0.00135
P( x < 47 )
= P( Z < (47-50)/1 )
= P( Z < - 3 )
= 0.00135
P( 47 < x < 53 )
= 1 - P( x > 53 ) - P( x < 47 )
= 1 - 2*0.00135
= 0.9973
= 99.73 % ..... Ans
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