3. (10 pts) Recently, cities have begun putting in place experimental programs to battle drugs, prostitution, and crime. These programs, sometimes derisively called "Hug a Thug", involve arresting violent drug dealers, setting high bail amounts, and using intense intervention with education, employment, and counseling to transform offenders from law-breakers to law-abiding citizens. You want to know if these programs actually reduce the number of crimes violent drug offenders commit upon release. Nationally, the average number of crimes committed by all inmates in the 6 months after release is 5 with a standard deviation of 1.68. You take a sample of 64 ex-inmates who completed the program and ask them how many crimes they committed in the 6 months since they were released.

a) (2 pts) What is the expected value of your sample mean?

b) (2 pts) What is the standard error for a sample of size 64?

c) (4 pts) You find that the average number of crimes committed by the sample of inmates who completed the program is 4.7. What is the probability of selecting a sample of size 64 with a mean less than 4.7? Draw a picture for full credit.

d) (2 pts) The governor wants to fund reentry programs that are highly effective. Should she fund this program? Explain your reasoning and be specific. An answer that is complete will use information from part c above.