A TV company receives numerous phone calls throughout the day from customers reporting service troubles and from would-be suscribers to the cable network. Most of these callers are put "on hold" until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 3.1 minutes and a standard deviation of 0.9 minutes. Company expersts have decided that if as many as 5% of the callers are put on hold for 4.8 minutes or longer, more operators should be hired.
(a) What proportion of the company's callers are put on hold for at least 4.8 minutes? Should the company hire more operators?
(b)At this company, 1% of the callers are put on hold for longer than k minutes. Find the value of k.