Please help me! A GE light bulb is supposed to last for 1,200 hours. In fact, light bulbs of this type last only 1,185 hours with a standard deviation of 70 hours. What is the probability that a randomly selected light bulb will have an average life of at least 1,200 hours?

Answer:0.016062.Step-by-step explanation:Assume that the population is normal:~(, 2) = (1185, 702).Then the distribution of the sample mean̅ =1 + 2 + 3 + ⋯ + 100100is exactly normal with mean̅= (̅) = = 1185 hoursand standard deviation̅= (̅) =√=70√100= 7 hours.The standardized variable =̅ − ̅̅=̅ − 11857Is distributed as (0,1).The following value of corresponds to the value ̅= 1200 of ̅: =̅−̅̅=1200−11857= 2.142857.Therefore,(̅ ≥ 1200) = (̅ − ̅̅≥1200 − ̅̅) = ( ≥1200 − 11857) = ( ≥ 2.142857) == 1 − ( < 2.142857) = 1 − 0.983938 = 0.016062,because using the command= NORM. S.DIST(2,142857; TRUE)from Microsoft Excel we can see that = 2.142857gives( < 2.142857) = 0.983938.Only rarely, just over one time in a hundred tries of 100 light bulbs, would the average life exceed 1200 hours