Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large (n > 30) random sample of annual incomes. Show all work if any. a. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not? b. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)? c. What value do the sample means target? That is, what is the mean of all such sample means?
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.
Annual incomes are known to have a distribution that is skewed to the right instead of being
a. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not?
b. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)?
c. What value do the sample means target? That is, what is the
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