Now focus on the statistics by Geographical Region. Consider three categories of
ID: 3170871 • Letter: N
Question
Now focus on the statistics by Geographical Region. Consider three categories of geographical regions: Texas (all of Texas, i.e. 70.10% of respondents), the Northeast, and all remaining regions. To obtain an estimate for the average salary in the “all remaining regions” category, calculate a simple arithmetic average salary in all regions in this category.
a) We randomly draw individual graduates of the school, identify their region of employment (by the three categories above) and consider the average salary the outcome of this random variable. Describe the probability model for this random variable. (3P)
b) What is the expected value for this random variable? (3P)
c) What is the standard deviation? (4P) The data provided are in US dollars. $1 US is currently worth approximately $1.3 Cdn
d) What is the expected value for this random variable in Canadian dollars? (2P)
e)bWhat is the standard deviation in Canadian dollars? (2P)
* The percentage of reports for Austin, Dallas, Houston, and Other Texas is a percentage of the overall Texas reports
Region Average Stanndard Deviation % of reports Mid-atlantic $54,460 $11,404 0.87% Midwest $61,850 $10,977 5.59% Northeat $73,180 $15,565 11.54% South $65,955 $12,583 2.10% Southwest $62,960 $7,095 0.87% West $67,363 $13,957 8.92% Texas 62,810 $11,731 70.10% Austin $54,811 $10,677 26.86%* Dallas $64,628 $9,475 35.91%* Houston $67,794 $11,546 34.41%* Other TX $54,182 $4,143 2.99%*Explanation / Answer
the expected value for this random variable in US $ = $62726.64
the standard deviation in US $ = $10832.09
the expected value for this random variable in Canadian dollars = 62726.64*1.3 = 81544.632 Cdn
the standard deviation in Canadian dollars = 10832.09 * 1.3 = 14081.717 Cdn
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