A manufacturer knows that their items have a normally
distributed length, with a mean of 16.5 inches, and standard
deviation of 3.1 inches.
If 9 items are chosen at random, what is the probability that their
mean length is less than 18.4 inches? (Give answer to 4 decimal
places.)
= 16.5 inches
= 3.1 inches
n = 9
For sampling distribution of mean, P( < A) = P(Z < (A - )/)
= = 16.5 inches
=
=
= 1.0333 inches
P(mean length is less than 18.4 inches) = P( < 18.4)
= P(Z < (18.4 - 16.5)/1.0333)
= P(Z < 1.84)
= 0.9671
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