A manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.5 minutes. a) After observing 100 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 95% confidence interval for the mean assembly time. b) How many workers should be involved in this study in order to have the mean assembly time estimated up to 15 seconds with 95% confidence