SOLUTION: A manufacturer knows that their items have a normally distributed length, with a mean of 18.3 inches, and standard deviation of 3.6 inches.
If 24 items are chosen at random, wha
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If 24 items are chosen at random, wha
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Question 1184623: A manufacturer knows that their items have a normally distributed length, with a mean of 18.3 inches, and standard deviation of 3.6 inches.
If 24 items are chosen at random, what is the probability that their mean length is less than 19.8 inches? (Give answer to 4 decimal places.) Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the population mean is 18.3 inches.
the population standard deviation is 3.6 inches.
the sample size is 24.
you want to know the probability that the sample mean is less than 19.8 inches.
standard error = standard deviation divided by square root of sample size = 3.6 / sqrt(24) = .7348469.
z = (x - m) / s
z is the z-score
x is the sample mean
m is the population mean
s is the standard error.
z = (19.8 - 18.3) / .7348469 = 2.0412415.
the area to the left of that z-score is equal to .9794, rounded to 4 decimal places.
