Your lumber company has bought a machine that automatically

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 (72 inches) with a standard deviation of 0.7 inch. Assume the lengths are normally distributed. You randomly select 44 boards and find that the mean length is 72.16 inches. Complete parts (a) through (c).

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

72.16? inches or more? Using your answer from part (a), what do you think of the seller\'s claim? Assuming the seller\'s claim is true, would it be unusual to have an individual board with that length? Use the z-score to determine if an individual board with this length is unusual?

(Round to four decimal places as needed.)

Solution

a)
Normal Distribution
Mean ( u ) =72
Standard Deviation ( sd )=0.7
Number ( n ) = 44
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 72.16) = (72.16-72)/0.7/ Sqrt ( 44 )
= 0.16/0.1055= 1.5162
= P ( Z <1.5162) From Standard NOrmal Table
= 0.9353                  
P(X > = 72.16) = 1 - P(X < 72.16)
= 1 - 0.9353 = 0.0647                  
b)
No it is not unusual, as the reason the required probability is
greater than 0.05