The following data are collected to study unemployment in a particular region in upstate New York. The first column shows the number of months unemployed and the second column shows the count of people in the study with the corresponing unemployment length. Let X be a random variable indicating the number of months a person is unemployed. a)Use the data to develop the probability mass function for X. b)Find the cumulative distribution function for X. c)Calculate the mean and standard deviation of X.
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.
Question 6:
The following data are collected to study unemployment in a particular region in upstate New York. The first column shows the number of months unemployed and the second column shows the count of people in the study with the corresponing unemployment length.
Let X be a random variable indicating the number of months a person is unemployed.
a)Use the data to develop the probability mass
b)Find the cumulative distribution function for X.
c)Calculate the mean and standard deviation of X.
| Months Unemployed | Number Unemployed |
| 1 | 1029 |
| 2 | 1686 |
| 3 | 2269 |
| 4 | 2675 |
| 5 | 3487 |
| 6 | 4652 |
| 7 | 4145 |
| 8 | 3587 |
| 9 | 2325 |
| 10 | 1120 |
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