Sampling Behavior of a count

#1
Undercoverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample. We can check for undercoverage by comparing the sample with known facts about the population.

a) Suppose we take an SRS of n= 500 people from a population that is 25% Hispanic. How many Hispanic are expected in a given sample?
b) What is the standard deviation for the number of Hispanics in the sample?
c) Can the normal approximation to the binomial be used to help make probabilistic statements about samples from this population? Why?
d) Determine the probability that a sample contains 100 or fewer Hispanics under the stated conditions (Include the curve)
e) Would you suspect undercoverate in a sample with 100 Hispanics? Explain your reasoning.