The accompanying data below represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. 32.7 35.9 38.0 38.6 40.1 42.0 34.4 36.2 38.1 38.9 40.6 42.8 34.8 37.3 38.3 39.2 41.4 43.4 35.3 37.6 38.5 39.4 41.7 49.2 (a) Compute the z-score corresponding to the individual who obtained 39.2 miles per gallon. Interpret this result The z-score corresponding to the individual is ____ and indicates that the data value is ____ standard deviation(s) above/below the mean./median. (Type integers or decimals rounded to two decimal places as needed.
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.
The accompanying data below represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
| 32.7 | 35.9 | 38.0 | 38.6 | 40.1 | 42.0 |
| 34.4 | 36.2 | 38.1 | 38.9 | 40.6 | 42.8 |
| 34.8 | 37.3 | 38.3 | 39.2 | 41.4 | 43.4 |
| 35.3 | 37.6 | 38.5 | 39.4 | 41.7 | 49.2 |
(a) Compute the z-score corresponding to the individual who obtained 39.2 miles per gallon. Interpret this result
The z-score corresponding to the individual is ____ and indicates that the data value is ____ standard deviation(s) above/below the
(Type integers or decimals rounded to two decimal places as needed.)
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