A manufacturer knows that their items have a normally distributed length, with a mean of 11.5 inches, and a standard deviation of 0.5 inches. If 19 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?
Solution :
Given that ,
mean =
= 11.5
standard deviation =
= 0.5
=
/
n = 0.5 /
19 = 0.1147
P(
< 11.2) = P((
-
) /
< (11.2 - 11.5) / 0.1147)
P(z < -2.6155)
= 0.0045
Probability = 0.0045
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