Question: Psychology and Human Behavior In attempting to flee from police, criminals often barricade themselves inside a building and create a police standoff. The criminal is usually armed with a dangerous weapon and may hold hostages. Suppose the mean length of a police standoff, ending with some sort of resolution, is 6.5 hours with standard deviation 4 hours. A random sample of 35 police standoffs is selected.
a. Find the distribution of the sample mean.
b. What is the probability that the sample mean for the 35 police standoffs will be greater than 7 hours?
c. A new psychological technique was used in negotiations with the criminals involved in the 35 police standoffs. Suppose the sample mean for the 35 police standoffs is x¯ = 5.1 hours. Is there any evidence to suggest that the mean police standoff time is lower when this new technique is used?