Chapter 5, Problem 5.69SE

Psychosomatic Problems A psychiatrist believesthat 80% of all people who visit doctors have problemsof a psychosomatic nature. She decides to select 25patients at random to test her theory.

1. Assuming that the psychiatrist’s theory is true, whatis the expected value of x. the number of the 25patients who have psychosomatic problems?
2. What is the variance of x, assuming that the theoryis true?
Find $P(x\le 14).$
3. (Use tables and assume that thetheory is true.)
4. Based on the probability in part e, if only 14 of the25 sampled had psychosomatic problems. What conclusions would you make about the psychiatrist’s theory? Explain.