15. show that a bounded linear operator t: h »h on a hilbert space h is normal if and only if ||t*x||= ||tx|| for all xeh. using this, show that for a normal linear operator, complex t°ll= |t|f

Monitors manufactured by tsi electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. if a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. round your answer to four decimal places.