Question 7 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
Two different furniture manufacturers produce chairs. Let X represent the number of chairs produced daily at plant X, and let Y represent the number of chairs produced daily at plant Y. Assume that X and Y are independent random variables. Which of the following choices explains the meaning of independent random variables in context?
Answer
A
The independence of the two manufacturers means that the two random variables have a correlation of 1.
B
The independence of the two manufacturers means that the number of chairs produced is approximately Normal.
C
The independence of the two manufacturers means that knowing how much one furniture plant produces does not help us predict how much the other produces.
D
The independence of the two manufacturers means that if one plant is producing chairs properly, the other has a smaller probability of producing chairs properly.
Explanation
Independent random variables provide no information about one another: knowing the daily number of chairs produced at plant X does not help predict the number produced at plant Y. Choice C states this meaning in context. Independence does not mean the variables have correlation 1 or that their distributions are approximately Normal.
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