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 4.2 years and a standard deviation of 0.6 years. He then randomly selects records on 38 laptops sold in the past and finds that the mean replacement time is 3.9 years. Assuming that the laptop replacement times have a mean of 4.2 years and a standard deviation of 0.6 years, find the probability that 38 randomly selected laptops will have a mean replacement time of 3.9 years or less.

You are in charge of the customer service phone line with many employees. at the end of each phone callthe customers are asked to rate their service from 1 to 5 stars, with 5 being the best. you find the averagerating for 20 randomly selected employees and decide you want to improve the ratings so you require thoseemployees to go through a new training program. you then wait a week and find the new average rating foreach employee. the average change is an increase in 1.3 stars with a standard devation of .9 stars.(a) is this data paired or not paired? (b) what are the null and alternative hypothesis being tested? (c) what is the t-statistic you would use? write the general formula and the final calculation.(d) sketch a t-distribution, label your t-statistic and the probability you would be interested in: