Your lumber company has bought a machine that automatically cuts lumber. The sel

Question

Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 6

feet(72inches) with a standard deviation of 0.6 inch. Assume the lengths are normally distributed. You randomly select 38 boards and find that the mean length is

72.2 inches. Complete parts (a) through (c).

(a) Assuming the seller's claim is correct, what is the probability that the mean of the sample is

72.2inches or more?

(Round to four decimal places as needed.)

(b) Using your answer from part (a), what do you think of the seller's claim?

The seller's claim appears to be(accurate or inaccurate) The sample mean (should or should not??) be considered unusual because, if the seller's claim is true, the probability of obtaining this sample mean is(less than 10%, greater then10%, less then 5% or greater then 5%)

less than 10%.

less than 5%.

greater than 5%.

greater than 10%.

(c) Assuming the seller's claim is true, would it be unusual to have an individual board with a length of72.2 inches? Why or why not?

(No,Yes,???)because72.2 (is,is not) within 2 standard deviations of the mean for an individual board.

Explanation / Answer

Mean length = 72 inches ( 6 feet )

Std dev = 0.6 inch

n = 50

sample mean = 72.21 inches

A)

Z score = ( Sample mean - true mean ) / (std dev / sqrt(n))

= (72.2 - 72) / (0.6/sqrt(50))

= 2.4749

P(X>=72.2) = 1 - P(X < 72.2) = 1 - P(Z = 2.4749) = 1 - 0.9932 = 0.0068

Thus the probability that the mean of the sample is 72.21 inches or more is 0.0068

B) The seller's claims are inaccurate because of such a small probability as obtained above

Sample mean should be not be considered unusual since it falls within 1 std deviation from the mean (<72+1*0.6)

c)Yes, because 72.2 is within 2 standard deviations of the mean for an individual board.

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