Binomial Distribution

1. A national study found that treating peopleappropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been difficult because it isestimated that 50% of hypertensives do not know that they have high bloodpressure, 40% of hypertensives who do know are inadequately treated by theirphysicians, and 50% who are adequately treated are noncompliant (fail to take theright number of pills).

Required:

a. What is the probability that among a randomly selected sample of 10 true hypertensives at least 50% are being treatedappropriately and are complying with this treatment?

b. What is the expected value for the number ofhypertensives adequately treated in this sample of 10?

c. What is the variance for the number ofhypertensives adequately treated?

d. What is the probability that at least 7 of the10 hypertensives know that they have hypertension?

e. What is the probability the at least 3, butfewer than 5 of the 10 hypertensives know that they have hypertension?

Provide justifications and citations for your responses.