6. (6 pts) A study of the amount of time it takes a mechanic to rebuild the tran

Question

6. (6 pts) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours. 7. (6 pts) A sample of 4 different calculators is randomly selected from a group containing 17 that are defective and 36 that have no defects. What is the probability that at least one of the calculators is defective? 8. (4 pts) The table below describes the smoking habits of a group of asthma sufferers Nonsmoker Occasional smoker Regular smoker Heavy smoker Total Men 384 Women 349 64 72 49 38 530 503 Total 733 136 87 1033 Ifone of the 1033 people is randomly selected, find the probability that the person is a man or a heavy smoker.

Explanation / Answer

6) here for std error =std deviation/(n)1/2 =1.8/(40)1/2 =0.2846

hence P(Xbar>8.7)=P(Z>(8.7-8.4)/0.2846)=P(Z>1.0541)=1-P(Z<1.0541)=1-0.8541=0.1459

7)

prbability that at least one is defective =1-P( none is defective)=1-(36/53)*(35/52)*(34/51)*(33/50)=0.7988

8)

probability=(530+38)/1033=0.5499

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