SOLUTION: No length of a lumber, a machine cuts are normally distributed by a mean of 89 inches and a standard deviation of 0.5 inch part a what is the probability that a randomly selected b

Question 1201038: No length of a lumber, a machine cuts are normally distributed by a mean of 89 inches and a standard deviation of 0.5 inch part a what is the probability that a randomly selected board cut by the machine has a length greater than 89.12 inches part B hey sample of 41 boards is randomly selected what is the probability that their main length is greater than 89.12 inches
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the lengths of lumber a machine cuts are normally distributed with a mean of 89 inches and a standard deviation of 0.5 inches.

part a:
what is the probability that a randomly selected board cut by the machine has a length greater than 89.12 inches.

part b:
what is the probability that a randomly selected sample of 41 boardshas a mean length greater than 89.12 inches.

answer to part a:
mean is 89 inches.
standard deviation is .5 inches.
probability that the board has a length greater than 89.12 inches is .4052.

answer to part b:
mean is 89 inches
standard deviation is .5
sample size is 41
standard error is .5 / sqrt(41) = .0780868809.
probability that the mean length of the sample will be greater thana 89.12 is .06217731.

when you are dealing with a sample of one element, use the standard deviation.
when you are dealing with the mean of a sample of more than 1 element, use the standard error.

the standard error is equal to the standard deviation divided by the square root of the sample size.

here's what the results look like on the calculator at https://davidmlane.com/hyperstat/z_table.html

display from patt a:

display from part b:

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