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6. (14 pts) Suppose nationwide that approximately 36% of adult Americans have nothing saved for retirement. A survey is conducted of a random sample of 100 adult Americans. Let X= the number of adult Americans who have nothing saved for retirement.

a. State the values of n and p for this binomial experiment. (2 pts.)

b. Find the probability that exactly 38 adults have nothing saved for retirement. Round to two decimal places and write the calculator function. (4 pts.)

c. Find the probability that 40 or fewer adults have nothing saved for retirement. Round to two decimal places and write the calculator function. (4 pts.)

d. Find the probability that at least 31 of the adults have nothing saved for retirement. Round to two decimal places and write the calculator function. (4 pts.)

8. (19 pts) Many veterans who bravely served in Iraq during Operation Enduring Freedom have developed symptoms of post-traumatic stress disorder (PTSD). A large study of returning veterans showed that 53% of the soldiers suffered from PTSD after serving in Iraq. A random sample of 200 veterans from Iraq were selected for additional research. Let X represent the number suffering from PTSD.

a. State the values of $n$ and $p$ for this binomial experiment. (2 pts.)

b. Compute the mean and standard deviation for X. Round to 2 decimal places. (5 pts.)

c. Verify whether or not the the distribution is approximately normally distributed ( 4 pts).

d. Compute the range of "usual" values for X. (4 pts.)

e. Would it be unusual to observe 75 soldiers suffering from PTSD? Why? (4 pts.)