Manufacturers of butter make sticks of butter that weigh 110 grams on average. A manufacturer suspects the machine that forms the sticks of butter may have a problem, so they weigh each stick of butter the machine produces in an hour. The weights are grouped into intervals of 0.5 grams and are summarized in a frequency table. weight (grams) frequency relative frequency 107–107.5 5 107.5–108 17 108–108.5 52 108.5–109 118 109–109.5 172 109.5–110 232 110–110.5 219 110.5–111 172 111–111.5 95 111.5–112 57 112–112.5 23 112.5–113 8 113–113.5 1 total 1,171
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Manufacturers of butter make sticks of butter that weigh 110 grams on average. A manufacturer suspects the machine that forms the sticks of butter may have a problem, so they weigh each stick of butter the machine produces in an hour.
The weights are grouped into intervals of 0.5 grams and are summarized in a frequency table.
| weight (grams) | frequency | relative frequency |
|---|---|---|
| 107–107.5 | 5 | |
| 107.5–108 | 17 | |
| 108–108.5 | 52 | |
| 108.5–109 | 118 | |
| 109–109.5 | 172 | |
| 109.5–110 | 232 | |
| 110–110.5 | 219 | |
| 110.5–111 | 172 | |
| 111–111.5 | 95 | |
| 111.5–112 | 57 | |
| 112–112.5 | 23 | |
| 112.5–113 | 8 | |
| 113–113.5 | 1 | |
| total | 1,171 |
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