A manufacturer knows that their items have a normally
distributed length, with a mean of 16.3 inches, and standard
deviation of 4.5 inches.
If 3 items are chosen at random, what is the probability that their
mean length is less than 15.1 inches?
Solution :
Given that,
mean =
= 16.3
standard deviation =
= 4.5
n = 3
= 16.3
=
/
n = 4.5
3 = 2.5981
P(
< 15.1 )
P (
-
/
) < ( 15.1 - 16.3 / 2.5981)
P ( z < -1.2 / 2.5981 )
P ( z < -0.46)
= 0.3228
Probability =0.3228
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