A pop music record firm wants the distribution of lengths of cuts on its records to have an average of 2 minutes and 15 seconds (135 seconds) and a standard deviation of 10 seconds so that disc jockeys will have plenty of time for commercials within each 5-minute period. The population of times for cuts is approximately normally distributed with only a negligible skew to the right. You have just timed the cuts on a new release and have found that the 10 cuts average 140 seconds.
a. What percentage of the time will the average be 140 seconds or longer if the new release is randomly selected?
b. If the music firm wants 10 cuts to average no longer than 140 seconds less than 5% of the time, what must the population mean be, given that the standard deviation remains at 10 seconds?