The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.5 years. He then randomly selects records on 55 laptops sold in the past and finds that the mean replacement time is 3.1 years.
Assuming that the laptop replacement times have a mean of 3.3 years and a standard deviation of 0.5 years, find the probability that 55 randomly selected laptops will have a mean replacement time of 3.1 years or less.
P(M < 3.1 years) =
