A Psychiatrist Believes That 90% of All People Who Visit

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.
Assuming that the psychiatrist's theory is true, what is the expected value of x, the number of the 20 patients who have psychosomatic problems?
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What is the variance of x, assuming that the theory is true?
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Find , assuming that the theory is true.
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Based on the probability in part (c), if only 14 of the 20 sampled had psychosomatic problems, what conclusions would you make about the psychiatrist's theory?
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Explain.
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