Question 1194872: The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.5% or more are defective, they call repair technicians for service.
The control department is going to take a random sample of 4400 light bulbs. Let be the proportion of defective light bulbs in the sample assuming the machinery is working correctly.
(a)Find the mean of p̂.
(b)Find the standard deviation of p̂.
(c)Compute an approximation for P(p̂ >0.015), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 4400*0.01=44=np units number of bulbs
the variance is np(1-p)=44*0.99=43.56 units # of bulbs^2
the sd is sqrt(43.56)=6.6 units number of bulbs
for 0.015% or 66 bulbs, an approximation would be z>(66.5-44)/6.6=3.41. I use 66.5 because of the continuity correction factor, and the number has to be greater than 66.
probability z>3.41 is 0.0003
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