The following is a question that is likely to be appear on my exam on Friday (tomorrow) but contextualised into a different scenario. I'm having serious difficulty figuring out how to go about answering it. If anybody has encountered something similar and could provide a step by step explanation on how to beget the answer, I would be wholly appreciative.
Dumpington is a commuter town, i.e. all those who work travel out of town to work. Its workforce consists of 60% men and 40% women. The distance that men travel to work follows a normal distribution with mean 10 miles and standard deviation 2 miles (all commuting distances are one-way). The distance that women travel to work follows a normal distribution with mean 6 miles and standard deviation 3 miles. (i) What is the probability that a randomly drawn worker travels between 9 and 7 miles to work? (ii) What is the proportion of the workforce that travels more than 12 miles to work?
I don't have emotions and sometimes that makes me very sad.
I presume you know how to calculate the probability of a value range for a normal distribution.
Split each problem into two separate cases, namely men and women. Then think about what the probability is that a randomly selected driver is a man or a woman and how this affects the calculation of--
P1 = Prob((Man and (7 < Dist < 9)) or (Woman and (7 < Dist < 9)))
P2 = Prob((Man and (Dist > 12)) or (Woman and (Dist > 12))).
(The bolded conjunctions imply specific arithmetic operations.)
Also think about how probabilities are related to proportions.
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