The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. 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 65 to 74 years of age in your state.

a. On the basis of the figure from the National Center for Health Statistics, what is the expected number of persons 65 to 74 years of age in your survey who have a chronic heart condition?

b. Suppose only one person in your survey has a chronic heart condition. What is the probability of getting one or fewer people with a chronic heart condition in a sample of 20 if 25% of the population in this age bracket has this health problem? What do you conclude about your state from the sample data?