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 7 feet ​(84 ​inches) with a standard deviation of 0.6 inch. Assume the lengths are normally distributed. You randomly select 45 boards and find that the mean length is 84.26 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  

84.2684.26

inches or​ more?

nothing

​(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.

inaccurate.

The sample mean

▼

should

should not

be considered unusual​ because, if the​ seller's claim is​ true, the probability of obtaining this sample mean is

▼

less than 5%.

less than 10%.

greater than 10%.

greater than 5%.

​(c) Assuming the​ seller's claim is​ true, would it be unusual to have an individual board with a length of

84.2684.26

​inches? Why or why​ not?

▼

No,

Yes,

because

84.2684.26

▼

is

is not

within 2 standard deviations of the mean for an individual board.

Answer 1

The​ seller's claim appears to be . The sample mean should be considered ​ because, if the​ seller's claim is​ true, the probability of obtaining this sample mean is .

because 84.26 within 2 standard deviations of the mean for an individual board.