The security department of a state university is planning its budget for the next year. In estimating the man-hours for security during university sponsored music concerts, the average length of music concerts is needed. A random sample from thirty-six security departments at universities was taken and the sample mean length of concerts was 160 minutes. Suppose the population standard deviation is 45 minutes. A 95 percent confidence interval for the true mean duration of music concerts is:
a. 157.55 to 162.45.
b. 147.63 to 172.37.
c. 71.8 to 248.2.
d. 145.3 to 174.7.
e. 160 1.96(45 / 36).