According to the U.S. Census Bureau, in 2011, the median (middle of the range) annual income of a high school graduate with no further education was about $35,400 per year. If we assume that it takes 4 years to earn a bachelor's degree and 2 additional years to earn a master's degree, the median annual income increases by 12% for each year spent toward successful completion of a degree. This describes a function  I = I(y),  where I is the median income in 2011 for a person with y years of college education. (a) Express in functional notation the median income in 2011 of an individual with a bachelor's degree, which requires 4 years of college. Calculate the value. (Round your answer to the nearest cent.) I       = $  (b) Make a table of values that shows the median income in 2011 for individuals completing 0 through 4 years of college. (Round your answers to the nearest cent.) Years of college Median income (in 2011) 0 $  1 $  2 $  3 $  4 $  (c) Make a graph of median income versus years of college completed. Be sure to provide appropriate labels.         (d) Verify that the formula  I = 35.4 × 1.12y  thousand dollars, where y is the number of years of college completed, gives the same values (to the nearest dollar) as those you found in the table you made. The formula yields the same values.The formula yields different values.     (e) Using the formula given in part (d), find the median income in 2011 of an individual who has a master's degree. (Round your answer to the nearest cent.) $  (f) Assuming it takes 3 years beyond the master's degree to complete a doctoral degree, and assuming the formula in part (d) applies, what was the median income of a person with a doctoral degree in 2011? (Round your answer to the nearest cent.) $  (g) In fact, the same rate of increase does not apply for the years spent on a doctoral degree. The actual median income was $91,000. Does that mean that the increase in median income for years spent earning a doctoral degree is higher or lower than 12% per year? higherlower

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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.