For unemployed persons in the United States, the average number of months ofunemployment at the end of December 2009 was approximately seven months(Bureau of Labor Statistics, January 2010). Suppose the following data are for aparticular region in upstate New York. The values in the first column show thenumber of months unemployed and the values in the second column show thecorresponding number of unemployed persons.MonthsUnemployedNumberUnemployed1 10292 16863 22694 26755 34876 46527 41458 35879 2325 10 1120Let x be a random variable indicating the number of months a person is unemployed.a. Use the data to develop an empirical discrete probability distribution for x.b. Show that your probability distribution satisfies the conditions for a validdiscrete probability distribution.c. What is the probability that a person is unemployed for two months or less?Unemployed for more than two months?d. What is the probability that a person is unemployed for more than sixmonths?
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.
For unemployed persons in the United States, the average number of months of
unemployment at the end of December 2009 was approximately seven months
(Bureau of Labor Statistics, January 2010). Suppose the following data are for a
particular region in upstate New York. The values in the first column show the
number of months unemployed and the values in the second column show the
corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1 1029
2 1686
3 2269
4 2675
5 3487
6 4652
7 4145
8 3587
9 2325
10 1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete
b. Show that your probability distribution satisfies the conditions for a valid
discrete probability distribution.
c. What is the probability that a person is unemployed for two months or less?
Unemployed for more than two months?
d. What is the probability that a person is unemployed for more than six
months?
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