SOLUTION: Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 gram

Question 805257: Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 grams. Quality control inspectors randomly select 16 parts, weigh each, and then compute the sample average weight for the 16 parts.
The probability that the mean weight of these 16 parts is more than 41 grams or less than
39 grams is

0.9772.
0.9544.
0.0228
.0456.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 grams. Quality control inspectors randomly select 16 parts, weigh each, and then compute the sample average weight for the 16 parts.
The probability that the mean weight of these 16 parts is more than 41 grams or less than 39 grams is
------
z(41) = (41-40)/(2/sqrt(16)) = 1/(1/2) = 2
z(39) = (39-40)/(2/sqrt(16)) = -1/(1/2) = -2
----
P(x > 41) = P(z>2 when df = 15) = normalcdf(2,100) = 0.0228
By symmetry P(x < 39) = 0.0228
Adding the 2 probabilities you get 0.0456
===========================
Cheers,
Stan H.
====================
0.9772.
0.9544.
0.0228
.0456.

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