Question 6.163

65. Women and Depression. According to the National Institute of Mental Health, nearly twice the proportion of women (12%) as men (6.6%) are affected by a depressive disorder each year. Suppose that random samples of five women and five men are taken. Let represent the number of women affected by a depressive disorder.

  1. Find and interpret the mean of .
  2. If possible, find the probability that equals the mean. If not possible, explain why it is not possible to do so.
  3. Construct the probability distribution graph of , and identify the mode of .
  4. Find the probability that equals the mode of .

6.2.65

(a) woman. If we repeat this experiment an infinite number of times, record the number of women affected by a depressive disorder for each sample, and take the mean of all the samples, the mean number of women living with a depressive disorder will equal . (b) Not possible. The expected value of is not an integer. (c) women

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(d) 0.5277