Question: 2. (6 + 24 = 30 points). The following table shows the results of a national survey of 200 executives who were asked to identify

2. (6 + 24 = 30 points). The following table shows the results of a national survey of 200 executives who were asked to identify the geographical location of their company and their company's industry type. Venn diagrams may be useful. Northeast (NE) Southeast (SE) Midwest (MW) West (W) Total 24 Finance (F) Manufacturing (M) Communications (C) Total 30 28 82 10 6 18 34 8 22 12 42 14 12 16 42 56 70 74 200 a. Create a joint and marginal probability table using the information given above. (5) Southeast (SE) Midwest (MW) West (W) Total Northeast (NE) Finance (F) Manufacturing (M) Communications (C) Total b. What is the probability that an executive is from the Northeast? c. What is the probability that an executive is in the Finance industry? d. What is the probability a person will be from the Northeast AND in Finance? e. What is the probability a person will be from the Northeast OR in Finance OR both? f. What is the probability a person will be neither from the Northeast nor in Finance? g. What is the probability a person will be in Finance, given that he or she is from the Northeast? h. Are Finance and being from the Northeast mutually exclusive? Explain. i. Are profession and location independent? Explain using probabilities

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