The scores on the Psychomotor Development Index (PDI), a scale of infant development, are approximately normal with mean 100 and standard deviation 15.

(a) An infant is selected at random. Find the probability that PDI is below 90.

(b) A study uses a random sample of 25 infants. Specify the sampling distribution of the sample mean PDI, and find the probability that the sample mean is below 90.

(c) Would you be surprised to observe a PDI score of 90? Would you be surprised to observe a sample mean PDI of 90? Why?

(d) Sketch the population distribution for the PDI. Superimpose a sketch of the sampling distribution for n = 25.