The manager of Portland Electronics store is concerned that his suppliers have been giving him TV sets with lower than average quality. His research shows that replacements times for TV sets have mean of 8.2 years and standard deviation of 1.1 years (based upon data from "Getting Things Fixed," Consumer Reports). He then randomly chooses 50 TV sets sold in the past and finds out that the mean replacement time is 7.8 years.
Supposing that TV replacement times have mean of 8.2 years and standard deviation of 1.1 years, find out the probability that 50 randomly chosen TV sets will have a mean replacement time of 7.8 years or less. Round the standard deviation you use to the nearest hundredth. Round the probability to the nearest thousandth.