The lengths of lumber a machine cuts are normally distributed with a mean of 9595 inches and a standard deviation of 0.70.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 95.3295.32 inches? (b) A sample of 4545 boards is randomly selected. What is the probability that their mean length is greater than 95.3295.32 inches?
The lengths of lumber a machine cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 95.32 inches?
Z value for 95.32, z =(95.32-95)/0.7 = 0.46
P( x >95.32) = P( z > 0.46)
=0.3228
(b) A sample of 45 boards is randomly selected. What is the probability that their mean length is greater than 95.32 inches?
Standard error = sd/sqrt(n) = 0.7/sqrt(45) =0.1044
Z value for 95.32, z =(95.32-95)/0.1044 = 3.07
P( mean x >95.32) = P( z > 3.07)
=0.0011
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