Faith and Healing. A higher percentage of southerners believe in God and prayer

Faith and Healing. A higher percentage of southerners believe in God and prayer, according to a 1998 study by the University of North Carolina's Institute for Research in Social Science. The survey was conducted by 413 adults in other states. One of the findings healed by prayer, compared with 28% of others. Assume that the results of the UNC survey are the true, population percentages for these regions. Suppose that 20 southerners are to be selected at random and asked if they believe they have been healed by prayer. We are interested in the number who answer "Yes" to this question. means of telephone interviews with 844 adults in 12 southern states and was that 46% of southerners believe they have been

a) What is an Clearly specify and define a random variable. (Let X = ...) State the model, verify conditions, and identify all parameters. appropriate statistical model?

b) Of the 20 southerners selected, what is the expected number of "Yes" responses? Write an expected value statement, give the formula, give the formula with numbers plugged in, give your final answer

For parts c), d), e), and f) write a probability statement and give a numerical answer.

c) What is the probability that exactly 10 responded "Yes"?

d) What is the probability that between 10 and 15 (both inclusive) responded "Yes"?

e) What is the probability that over 75% of the 20 responded "Yes"?

f) What is the probability that less than 8 responded "Yes"?

g) Suppose a sample of 100 non-southerners were to be selected at random and asked if they believe they have been healed by prayer. What is the expected number of "Yes" responses and what is the standard deviation for the number of "Yes" responses?