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 9 feet (108 inches) with a standard deviation of 0.4 inch. Assume the lengths are normally distributed. You randomly select 47 boards and find that the mean length is 108.12 inches. Complete parts (a) through (c). Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table (a) Assuming the seller's claim is correct, what is the probability that the mean of the sample is 108.12 inches or more? (Round to four decimal places as needed.)

Explanation / Answer

Mean is 108 and s is 0.4 here N=47 thus standard error se=s/sqrt(N) =0.4/sqrt(47)=0.058

P(x>108.12) =P(z>(108.12-108)/0.058)=P(z>2.07) or 1-P(z<2.07)

thus from normal distribution table we get 1-0.9808=0.0192

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