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?
During monsoon season in India, the mean amount of rainfall is 89 centimeters.12 Suppose the standard deviation is 5 centimeters and 30 monsoon seasons are selected at random.
a. What is the probability that the sample mean rainfall is less than 87 centimeters?
b. What is the probability that the sample mean rainfall is greater than 91.5 centimeters?
c. Find a symmetric interval about the mean, 89, such that the probability that the sample mean lies in this interval is 0.90.
Carbon dioxide (CO2) is one of the primary gases contributing to the greenhouse effect and global warming. The mean amount of CO2 in the atmosphere for March 2013 was 397.34 parts per million (ppm).13 Suppose 40 atmospheric samples are selected at random in May 2013 and the standard deviation for CO2 in the atmosphere is s 5 20 ppm.
a. Find the probability that the sample mean CO2 level is less than 393 ppm.
b. Find the probability that the sample mean CO2 level is between 395 and 403 ppm.
c. Suppose the sample mean CO2 level is 400. Is there any evidence to suggest that the population mean CO2 level has increased? Justify your answer.