A widely used measure of infant development is the Psychomotor Development Index (PDI).Since the PDI has been used so frequently, we have a pretty good idea of the population mean and population standard deviation for scores on the PDI.The population mean is 100, and the population standard deviation is 15.Given this, what is the probability that:

a) In a sample of 100 infants, the sample mean PDI score is 101 or greater.

b) In a sample of 100 infants, the sample mean PDI score is 98 or less.

c) In a sample of 36 infants, the sample mean PDI score is 98 or less.

(2 points each)

a) Mean = 100

SD =15/100 = 1.5

P(X>102)=P(X>102100)=P(X>1.5102100) =P(Z>1.33)=0.0918

b)

P(X<103)=P(X<103100)=P(X<1.5103100) =P(Z<2)=0.9772

c)

Mean = 100

SD =15/36= 2.5

P(X<103)=P(X<103100)=P(X<2.5103100) =P(Z<1.2)=0.8849

Because of sample size, they are different 100 and 36.

********************************************

4.Explain why the probability for getting a mean PDI score of 98 or less in question 3 differs between parts b and c.