Given a normal distribution with μ= 101 and σ = 20, and given you select a sample of equals =16
What is the probability that X is above 102.6?
P (X > 102.6) =
We have to find P( > 102.6 )
We have to use following property ,
If sample size n drawn from normal distribution with mean and standard deviation then distribution of sample mean is approximately normal with mean = = and standard deviation |
We are given , = 101 , = 20 , n = 16
So, Mean of = = = 101
Standard deviation of = = 20/sqrt(16) = 5
We have to find P( > 102.6 )
P( > 102.6 ) = 1 - P( < 102.6 )
Using Excel function , =NORMDIST( x, mean , standard deviation , 1 )
P( < 102.6 ) = NORMDIST( 102.6 , 101 , 5 , 1 ) = 0.6255
So, P( > 102.6 ) = 1 - 0.6255 = 0.3745
P( > 102.6 ) = 0.3745
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