Q1) One of the factors which a company will use in finding whether it will locate new facility in a community is status of real estate market. Managers believe that significant measure of real estate market is average length of time that homes stay on market before selling.  They think that if mean time on market is less than 45 days, real estate market is favourable. To test this in particular area, a random sample of n = 100 homes which sold in past six months was selected. Mean for this sample was 40 days. It is believed that population standard deviation is 15 days. If test is conducted using 0.05 level of significance, what conclusion must be reached?

Q2) State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, like scales, are correct so customers and businesses are not cheated.  Periodically, employees of department go to businesses and test their scales.  For instance, dairy bottles milk in 1-gallon containers.  Assume that if filling process is working accurately, mean volume of all gallon containers is 1.00 gallon with standard deviation equal to 0.10 gallons.  Based on this information, if department employee selects random sample of n = 9 containers, determine probability that mean volume for sample will be greater than 1.01 gallons?  

a) 0.3821

b) 0.1179

c) 0.6179

d) 0.2358