Assume the number of years in prison before being exonerated is normally distributed for both white and black males. The average amount of time Black males are in prison before being exonerated is 13.7 years with a population standard deviation of 9.8 years. The average amount of time White male are in prison before being exonerated is 9.2 years with a population standard deviation of 8.6. Give all answers to at least 2 decimal places. If a White male is at the 70th percentile for years in prison before being exonerated, find the time the person has been in prison. years
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 following information is slightly different for each student but very close to the actual real data.
Assume the number of years in prison before being exonerated is
The average amount of time Black males are in prison before being exonerated is 13.7 years with a population standard deviation of 9.8 years. The average amount of time White male are in prison before being exonerated is 9.2 years with a population standard deviation of 8.6. Give all answers to at least 2 decimal places.
If a White male is at the 70th percentile for years in prison before being exonerated, find the time the person has been in prison.
years
From the provided information,
Mean and standard deviation of time White male are in prison as follow:
µ = 9.2 years
σ = 8.6 years
Let X be a random variable which represents the amount of time White male has been in prison.
X~N (9.2, 8.6)
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