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è Secure https://utexas.instructure.com/courses/1214644/quizzes/1180605/take Grades Quiz Instructions Question 4 Question5 ectures Online odules Clicker uizzes Objective To understand the effects of linear transformations on the mean, variance (and standard deviation), and covariance Time Elapsed: Hide Attempt due: Feb 1 at 3:15p 20 Hours, 46 Minutes Seconds An automobile manufacturer produces and sells the Energy-Saver Car in North America. It also produces and sells the Smart Little Car in China In North America, the mean annual number of Energy Saver Cars produced over the past decade was 12,100. The variance was 8,100. Net revenue for each car sold was $2.1 thousand. (Net revenue is price minus unit variable costs.) The annual fixed costs of the North American facilities were $176 thousand (costs of management, buildings, insurance, etc.) In China, the mean annual number of Smart Little Cars produced over the past decade was 7,500 The variance was 6,400. Net revenue for each car sold was $1.2 thousand. The annual fixed costs of the facility in China were $23 thousand. The covariance between the number of cars produced in North America and the number of cars produced in China was 5,040 Use X and Y to represent the number of cars produced in North America and the number produced in China, respectively. Use PRX and PRY to represent profits in North America and profits in China, respectively

Explanation / Answer

1)

sd of profit of North America = 2.1* sqrt(Variance of numberof car) = 2.1* sqrt(8100) = 90*2.1 = 189

2) variance of profit of China = 6400 *1.2^2=9216

3) Covariance = 5040*1.2*2.1= 12700.8

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