A random sample of 50 gas stations in Cook County, Illinois, resulted in a mean price per gallon of $2.60 and a standard deviation of $0.07. State the Empirical Rule. A histogram of the data indicates that the data follow a bell-shaped distribution. Use the Empirical Rule to determine the percentage of gas stations that have prices within three standard deviations of the mean. Determine the percentage of gas stations that have prices between $2.46 and $2.74, according to the Empirical Rule. Explain your calculations. Would a gas price of $2.99 be considered unusual in the statistical sense? Why or why not?
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.
A random sample of 50 gas stations in Cook County, Illinois, resulted in a mean price per gallon of $2.60 and a standard deviation of $0.07.
- State the Empirical Rule.
- A histogram of the data indicates that the data follow a bell-shaped distribution. Use the Empirical Rule to determine the percentage of gas stations that have prices within three standard deviations of the mean.
- Determine the percentage of gas stations that have prices between $2.46 and $2.74, according to the Empirical Rule. Explain your calculations.
- Would a gas price of $2.99 be considered unusual in the statistical sense? Why or why not?
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