Paranoid schizophrenics often manifest two different types of problems: depression and trembling. Following is the probability distribution for a discrete random variable, X: the number of these problems that a paranoid schizophrenic might experience:

X P(X)
0 .35
1 .47
2 .18

a) Generate the sampling distribution for the mean number of these problems that random samples of two paranoid schizophrenics might experience.

b) What are the mean and standard deviation of the sampling distribution of the mean number of these problems that samples of 40 paranoid schizophrenics might experience?

c) What is the probability that the total number of these problems in a random sample of 40 paranoid schizophrenics will exceed 36?

a) 0.83
b) 0.1119
c) 0.2643