SOLUTION: I have a standard error of mean question that I am having a hard time setting up. A grain mill manufactures 100 pound bags of flour, weights of bags are normally distributed with a

Question 693105: I have a standard error of mean question that I am having a hard time setting up. A grain mill manufactures 100 pound bags of flour, weights of bags are normally distributed with a mean of 100 pounds and standard deviation of 15 pounds.
So I have xbar/mean=100 and standard deviation=15 (not even sure if my set up is correct)

I am trying to calculate the Probability that the weight selected falls between 94 and 106 pounds as well as...
...the Probability that the sample of 36 bags which will be n=36 has a mean weight between 94 and 106 pounds.
I am trying to use the normal distribution table to locate zscore but I just can not figure it out. I think I am using the wrong method to compute these problems
I am returning adult who has not touched math in over 20 years, thanks for any guidance you can provide
thank you :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have a standard error of mean question that I am having a hard time setting up.
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A grain mill manufactures 100 pound bags of flour. Weights of bags are normally distributed with a mean of 100 pounds and standard deviation of 15 pounds.
---------
I am trying to calculate the Probability that the weight selected falls between 94 and 106 pounds as well as...
-----
Determine the z-score of 94 and or 106.
z(94) = (94-100)/15 = -6/15 = -2/5 = -0.4
----------------------------
z(106) = (106-100)/15 = 6/15 = +0.4
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P(94<= x <=106) = P(-0.4<= z <=0.4) = 0.3108
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...the Probability that the sample of 36 bags which will be n=36 has a mean weight between 94 and 106 pounds.
---
Note: The std for the distribution of
sample means is 15/sqrt(36) = 15/6 = 5/2
===================
z(94) = (94-100)/(5/2) = -6/(5/2) = -12/5 = -2.8
z(106) = (106-100)/(5/2) = +2.8
----
P(96<- x-bar <=106) = P(-2.8<= z <=2.8) = 0.9949
===================================================
Comment: You will probably need a good calculator to
continue your Statistics study. I find the TI-84 plus
does an excellent job.
====================
Cheers,
Stan H.
=======================

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