Suppose that the ifetimes of light bulbs are appraximately nomally distributed,

Question

Suppose that the ifetimes of light bulbs are appraximately nomally distributed, with a mean of 57 hours and a standard deviation of 3.5 hoirs. With this information, anower the following quetiones (a) What proportion of light bulbs will last more than 60 hours? (b) What proportion of light bulbs will last 51 hours or less? (c) What proportion of ight bulbs will last between 57 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 60 hours is 0.1957 Round to four decimal places as needed) (b) The proportion of light bulbs that last 51 hours or less is Round to four decimal places as needed) Enter your answer in the answer box and then click Check Answer 2 Pernsining O Type here to search F11 ·F10 F9 F7 F8 F6 F4 F3 F2 8 7 8 6

Explanation / Answer

Solution:-

a) p(x>60)

z = (60-57)/3.5 = 0.86

P(z > 0.86 ) = 1-0.8051 = 0.1949

b) P(x<51)

z = (51-57)/3.5 = -1.7142

P(z<-1.7142) =1P ( Z<1.7142 ) = 10.9564 = 0.0436

c) P(57<x<62)

z1 = (57-57)/3.5 = 0

z2=(62-57)/3.5 = 1.43

P(0<z<1.43) = 0.9236-0.5 = 0.4236

d) P(x<45)

z=(45-57)/3.5 = -3.4286

P(z<-3.4286) = 10.9997 = 0.0003

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