Question

A population of values has a normal distribution with μ=139.8μ=139.8 and σ=23σ=23. You intend to draw a random sample of size n=12n=12.

Find the probability that a single randomly selected value is greater than 155.1.
P(X > 155.1) =

Find the probability that a sample of size n=12n=12 is randomly selected with a mean greater than 155.1.
P(M > 155.1) =

Answer 1

Given ,

Mean = = 139.8   , standard deviation = = 23 , sample size = n = 12

a )

We have to find P( x > 155.1 )

P( x > 155.1 ) = 1 - P( x <= 155.1 )

Using Excel function ,   =NORMDIST( x , mean , standard deviation , 1 )

P( x <= 155.1 ) = NORMDIST( 155.1 , 139.8 , 23 , 1 ) = 0.747044

So, P( x > 155.1 ) = 1 - 0.747044 = 0.25296

b )

We have to find P( >= 155.1 )

Mean of = = 139.8

Standard deviation of = = = 6.63953

P( > 155.1 ) = 1 - P( <= 155.1 )

Using Excel function ,   =NORMDIST( x , mean , standard deviation , 1 )

P( <= 155.1 ) = NORMDIST( 155.1 , 139.8 , 6.63953 , 1 ) = 0.989399

So, P( > 155.1 ) = 1 - 0.989399 = 0.0106