Question

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) =

Answer 1

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