# Question

The scores on the Psychomotor Development Index (PDI), a scale of infant development, have a normal population distribution with mean 100 and standard deviation 15. An infant is selected at random.

a. Find the z -score for a PDI value of 90.

b. A study uses a random sample of 225 infants. Using the sampling distribution of the sample mean PDI, find the z -score corresponding to a sample mean of 90.

c. Explain why a PDI value of 90 is not surprising, but a sample mean PDI score of 90 for 225 infants would be surprising.

a. Find the z -score for a PDI value of 90.

b. A study uses a random sample of 225 infants. Using the sampling distribution of the sample mean PDI, find the z -score corresponding to a sample mean of 90.

c. Explain why a PDI value of 90 is not surprising, but a sample mean PDI score of 90 for 225 infants would be surprising.

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