A group of psychologists examined the effect of alcohol on the reactions to a threat. After obtaining a blood alcohol level (BAL) of at least 0.015 mg/cl, experimental subjects were placed in a room and threatened with electrical shocks. Using sophisticated equipment to monitor the subjects' eye movements, the startle response (measured in milliseconds) was recorded for each subject. The mean and standard deviation of the startle responses were 37.9 and 12.4, respectively. Assume that the startle response X for a person with a BAL of at least 0.015 is approximately normally distributed.

(a) Find the probability that X is between 40 and 50 milliseconds.

(b) Find the probability that X is less than 30 milliseconds.

(c) Give an interval centered about the mean of 37.9 milliseconds that contains 95% of startle responses (in milliseconds) for subjects with a blood alcohol level (BAL) of at least 0.015.(Hint: Find first the value z such that P(?z ? Z ? z) = 0.95 where Z is N(0, 1).