LED bulbs claim to last much longer than other types of bulbs. When LED bulb manufacturers come up with the number of hours that an LED bulb can last, that number actually includes a little bit of time where the bulb is slowly degrading. LED bulb lifetimes are actually normally distributed with a mean lifespan of 20000 hours and a standard deviation of 1200 hours. Mean (P) = hrs Standard Deviation (o) = hrs A) If an LED lightbulb is randomly selected, calculate the probability that its lifespan will be: (i) less than 18000 hours X = hrs z score = Probability p (x S 18000) = %(ii) greater than 23000 hours X = hrs z score = Probability p (x S 23000) = Probability p (x 2 23000) = (ii) between 16500 and 21500 hours X = hrs X= hrs z score = z score = Probability p (x $ 16500) = Probability p (x $ 21500) = Probability p (16500 S x S 23000) = % B) Determine the bulb lifespan corresponding to the: Mean () = hrs Standard Deviation (0) = hrs(i) For 90111 percentile Probability (p): l ' 4 decimal places ZSGOFE 2' x=l The life span of the bulb to be in 90'h percentile is hrs (ii) For middle 70% of LED bulbs for middle 70% Probability lies between % to ' % P1: 4 '4 decimal places P2:'l 4 decimal places Z1=l l 22=l X1 :' ' X2 :' Far middle 70% the life span of the LED bulb lies between ' ' hrs to ' 'hrs