Question

Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information answer the following questions. (a) What proportion of light bulbs will last more than 62 hours? (b) What proportion of light bulbs will last 50 hours or less? (c) What proportion of light bulbs will last between 58 and 62 hours? (d) What is the probability that a randomly selected light bulb lasts less than 45 hours? (a) The proportion of light bulbs that last more than 62 hours is (Round to four decimal places as needed) (b) The proportion of light bulbs that last 50 hours or less is (Round to four decimal places as needed.) (c) The proportion of light bulbs that lasts between 58 and 62 hours is (Round to four decimal places as needed.) (d) The probability that a randomly selected light bulbs lasts less than 45 hours is (Round to four decimal places as needed.)

Answer 1

Answer ö- - Xi lifetimes of light bulbs XNN(M=57, o=3.5) zu X-4_N N(0,12 a) > we want to find ex>62) = P(X-M 62-57 3.5 = P(Z > 1.4286) = 0.0766 (from normal Pyob. table) that last more than 62 hours of light bulbs The is proportion 0.0766 b7 * we want to find, P (X<50) = P(x-41 < 50-54) we want 50-57 -= P(Z<-2) = 0.0228 (from normal prob. table) of light bulbs that last 50 hours or less The proportion is 10.02287 CI -- we want to find P (58 < X < (2) SL (0.2857 Zz < 1.4286) = 0.311 m normal prob. table)

that lasts between 58 and The proportion of light bulbs 62 hours is 10.3110] d] - we want to find P(x <45) = P(X-M To < 45-57) 3.5 = P(Z <-3.42802 = 0.0003 (from normal . Prob. table) The probability that a randomla Selected light bulbs last less than 45 hours is 0.0003