posted by Samantha on .
A pop-music record firm wants the distribution of lengths of cuts on its record to have an average of 129 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 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 15 cuts average 149 seconds.
What percentage of the time will the average be 149 seconds or longer if the new release is randomly selected? (Give your answer correct to four decimal places.)
(b) If the music firm wants 15 cuts to average 149 seconds less than 5% of the time, what must the population mean be, given that the standard deviation remains at 10 seconds? (Give your answer correct to one decimal place.)