At Goldey-Beacom College, 56% of employees carry dependent family members on their health insurance plans. Currently, there are 200 employees working for the college. A random sample of 50 employees is selected.
a) What is the probability that less than 60% of the sample carries dependent family members on their health insurance plan?
b) Answer the question in part a using sample sizes of 100 and 150. Explain the differences in these probabilities.
c) Answer the question in part a without the finite correction factor. Explain the differences in these probabilities.