The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 85,000. Suppose that 70% of the before-tax family incomes when the head of the household has a college degree are between $75,500 and $94,500 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree?
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 Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 85,000. Suppose that 70% of the before-tax family incomes when the head of the household has a college degree are between $75,500 and $94,500 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree?
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