Question

A manufacturer knows that their items lifespans are normally distributed according to N ( 13.1 ,...

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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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) =

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