It is generally believed that electrical problems affect about14% of new cars.An

Question

It is generally believed that electrical problems affect about14% of new cars.An automobile mechanic conducts diagnostic tests on128 new cars on the lot. a) Describe the sampling distribution for the sampleproportion by naming the model and telling its mean and standarddeviation.Justify your answer. b)What is the probability that in this group over 18% of thenew cars will be found to have electrical problems? It is generally believed that electrical problems affect about14% of new cars.An automobile mechanic conducts diagnostic tests on128 new cars on the lot. a) Describe the sampling distribution for the sampleproportion by naming the model and telling its mean and standarddeviation.Justify your answer. b)What is the probability that in this group over 18% of thenew cars will be found to have electrical problems?

Explanation / Answer

Binomial distribution, n= 128 , p=.14, q=.86 =np=17.92, =(npq)=3.93 B) if 18% are defective then 128*.18=23.04 and we require P(x>23.04)=ans where x is binomial described above Let y be normal with =17.92 and =3.93 ans= P(y>23.5) the correction to 23.5 is used because x isdiscrete and x>23.04 would imply x=>24, but y is continuousso y>23.5 would be the same as x=>24 ans= (z>(23.5-17.92)/3.93)=P(z>1.42)=.5-P(0

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