Question

A manufacturer knows that their items lifespans are normally distributed according to

N

(

13.1

,

0.9

)

N

(

13.1

,

0.9

)

.

What proportion of the items' lifespans will be longer than 14 years?

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Enter your final answer below, Round to 4 decimal places.

Answer 1

X follows a Normal distribution with mean = 13.1 and S.D = 0.9 Then z=(x-mean)/SD = (x-13.1)/0.9 follows standard Normal.

When x=14, z=(14-13.1)/0.9 = 1 P(Z< 1) =0.8413 [using Normal table or Excel : NORM.S.DIST(1, TRUE)] P(X> 14 ) = 1-PCX < 14) = 1-P(Z < 1) = 1-0.8413 = 0.1587