b) A psychiatrist believes that 90% of all people who visit doctors have problems of a psychosomatic nature. She decides to select 20 patients at random to test her theory. Let the random variable x denotes the number of patients who do not have the psychosomatic problem.

(i) Assuming that the psychiatrist's theory is true, what is the expected value of x, the number of the 20 patients who do not have psychosomatic problems?

(ii) What is the variance of x, assuming that the theory is true?

(iii) Find P(x < 4), assuming that the theory is true.

(iv) Find Find P (2 < X <=8), assuming that the theory is true.

(v) Find P(x > 3), assuming that the theory is true.