7. + -12.25 points MBasicStat7 13.E·012. My Notes Ask Your Teacher A university

Question

7. + -12.25 points MBasicStat7 13.E·012. My Notes Ask Your Teacher A university organization shows that 108 of the university's 253 assistant professors were women, along with 91 of the 301 associate professors and 72 of the 350 full professors. (a) What is the probability that a randomly chosen university professor (of any rank) is a woman? (Round your answer to four decimal places.) (b) What is the conditional probability that a randomly chosen professor is a woman, given that the person chosen is a full professor? Round your answer to four decimal places.) (c) Are the rank and sex of the university professors independent? How do you know? O Rank and sex are not independent because the probabilities P(woman) and P(full professors) are not the same O Rank and sex are independent because the probabilities P(full professor), P(associate professors) and P(assistant professors) are not helpful for computing P(woman). O Rank and sex are independent because the probabiies in (a) and (b) are not equal O Rank and sex are independent because the probabilities P(woman) and P(full professors) are the same. O Rank and sex are not independent because the probabilities in (a) and (b) are not equal.

Explanation / Answer

Ans:

a)P(woman)=271/904=0.2998

b)P(woman/full prof)=P(woman and full prof)=72/350=0.2057

c)Rank and sex are not independent because the probabilitis in a) and b) are not equal

Asst. prof assc. Prof full prof Total women 108 91 72 271 men 145 210 278 633 Total 253 301 350 904

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