The standard deviation of the weight of filled salt containers is 0.4 ounce. If 2.5 percent of
Question:
The standard deviation of the weight of filled salt containers is 0.4 ounce. If 2.5 percent of the containers contain less than 16 ounces, what is the mean filling weight of the containers?
Salt Containers | |||||||||||
X-value Calculations Given Probabilities Using the Inverse Normal Distribution - Template | |||||||||||
This spreadsheet is designed to calculate the X-value based on probability of values equal to, or less than a desired x value, | |||||||||||
of a normally distributed variable. It requires input of a known mean and standard deviation and uses the inverse of the cumulative normal distribution | |||||||||||
Enter the mean of the distribution in cell D10 and the standard deviation in cell D11, below. | |||||||||||
Enter the desired probability in cell D12, and the calculated x-value will be seen in D13. | |||||||||||
Mean of distribution | 16.784 | ||||||||||
Std Dev of distribution | 0.4 | ||||||||||
Probability of X or less | 0.025 | ||||||||||
Calculated X-Value | 16.00 | ||||||||||
Calculated x-values | Probability | ||||||||||
15.184 | 0.00003 | ||||||||||
15.224 | 0.00005 | ||||||||||
15.264 | 0.00007 | ||||||||||
15.304 | 0.00011 | ||||||||||
15.344 | 0.00016 | ||||||||||
15.384 | 0.00023 | ||||||||||
15.424 | 0.00034 | ||||||||||
15.464 | 0.00048 | ||||||||||
15.504 | 0.00069 | ||||||||||
15.544 | 0.00097 | ||||||||||
15.584 | 0.00135 | ||||||||||
15.624 | 0.00187 | ||||||||||
15.664 | 0.00256 | ||||||||||
15.704 | 0.00347 | ||||||||||
15.744 | 0.00466 | Truncated | |||||||||
15.784 | 0.00621 | x-values | Probability | ||||||||
15.824 | 0.00820 | 15.184 | 0.00003 | ||||||||
15.864 | 0.01072 | 15.584 | 0.00135 | ||||||||
15.904 | 0.01390 | 15.984 | 0.02275 | ||||||||
15.944 | 0.01786 | 16.384 | 0.15866 | ||||||||
15.984 | 0.02275 | 16.784 | 0.50000 | ||||||||
16.024 | 0.02872 | 17.184 | 0.84134 | ||||||||
16.064 | 0.03593 | 17.184 | 0.84134 | ||||||||
16.104 | 0.04457 | 17.984 | 0.99865 | ||||||||
16.144 | 0.05480 | 18.384 | 0.99997 | ||||||||
16.184 | 0.06681 | ||||||||||
16.224 | 0.08076 | ||||||||||
16.264 | 0.09680 | ||||||||||
16.304 | 0.11507 | ||||||||||
16.344 | 0.13567 | ||||||||||
16.384 | 0.15866 | ||||||||||
16.424 | 0.18406 | ||||||||||
16.464 | 0.21186 | ||||||||||
16.504 | 0.24196 | ||||||||||
16.544 | 0.27425 | ||||||||||
16.584 | 0.30854 | ||||||||||
16.624 | 0.34458 | ||||||||||
16.664 | 0.38209 | ||||||||||
16.704 | 0.42074 | ||||||||||
16.744 | 0.46017 | ||||||||||
16.784 | 0.50000 | ||||||||||
16.824 | 0.53983 | ||||||||||
16.864 | 0.57926 | ||||||||||
16.904 | 0.61791 | ||||||||||
16.944 | 0.65542 | ||||||||||
16.984 |
Transcribed Image Text:
Probability 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 15 15.5 X-values vs. Cumulative Probability 16 16.5 17 X-values 17.5 18 18.5 19 -Series1
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An Introduction To Six Sigma And Process ImprovementISBN: 9781133604587 2nd Edition Authors: James R. Evans, William M. Lindsay
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