According to ABS data, 40% of Australians above the age of 65 have chronic heart disease. Suppose you live in a state where the environment is conducive to good health and low stress, and you believe the conditions in your state promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 20 persons over 65 years of age in your state.

(a) On the basis of the figure from the ABS, what is the expected number of persons in your survey who have chronic heart disease?

(b) Suppose only 1 person in your survey has chronic heart disease. What is the probability of finding 1 or fewer people with chronic heart disease in a sample of 20 if 40% of the population in this age bracket have this health problem? What do you conclude about your state from the sample data?