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 52 hours or​ less? ​(c) What proportion of light bulbs will last between 57 and 61 ​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 nothing. ​(Round to four decimal places as​ needed.)

Answer 1

we have given   and and let x is the  lifetimes of light bulbs and

a) P(x> 62 ) =P (z> (62 - 57)/3.5 ) = 0.0766

0.0766 proportion of light bulbs will last more than 62 ​hours

b) P(x 52 ) = P (z (52 - 57)/3.5 ) = 0.0766

0.0766 proportion of light bulbs will last 52 hours or​ less .

c) P (57 x 61) = P (57 - 57)/3.5 z (61- 57)/3.5 )  

P (57 x 61) =0.3735

the proportion of light bulbs will last between 57 and 61 ​hours is 0.3735

d) P(x 45 ) = P (z (45 - 57)/3.5 ) =.0003

the probability that a randomly selected light bulb lasts less than 45 ​hours is 0.0003