Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16.5...

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.)

Homework Answers

Answer #1

= 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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