1. Suppose a population follows a normal distribution and has a mean of = 125 an

Question

1.Suppose a population follows a normal distribution and has a mean of = 125 and a standard deviation of =24.

a.For samples of size n=4, Find the probability of observing a sample mean of less than 132 i.e. P( x 132 ) =

b.For samples of size n=16, Find the probability of observing a sample mean of more than 131, i.e. P( x 131) =

c.For samples of size n=36, Find the probability of observing a sample mean between 122 and 127.5            i.e. P(122 x 127.5) =   

Explanation / Answer

given mean =125 standard deviation = 24

n = 4

a) z= x^ - mean ) / Standard deviation

Z= (132 - 125 )/24 =0.04

P( x 132 ) =P(z<0.04)=0.5160 from standard normal z table

b) Z =131-125) / 24 = 0.25

P( x 131) = P(z>=0.25)=1-p(z<=0.25)=1-0.5987=0.4013

c) Z 1= 127.5 -125 ) /24 =0.1041

Z2= 122-125 )/24 = -0.125

P(122 x 127.5) = P(z1-z2) = 0.5557 -0.4522=0.1035

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