a bulb is picked at random from the 40000 bulbs. find the probability that the bulb is defective

Question

an inspections shows that are of 40000 bulbs produced by a factory, at 800 are defective. a) a bulb is picked at random form from the 40 thousand bulb. find the probability that the bulb is defective. b) if 1000 bulbs are picke dat random from the 40000 bulb how many bulbs are expcted to be defective

Answer 1

The probability of picking one defective bulb out of 40,000 bulbs when 800 are defective (1 out of 50) is 1/50 or 0.02. 

The expected number of defective bulbs in 1,000 picked randomly should, on average, approximate to 0.02*1000=20.

Applying a binomial distribution, mean=40000/50=800 and standard deviation is sqrt(40000*0.02*0.98)=28 (this is an application of mean=np, s.d.=sqrt(np(1-p)) where n=40000, p=0.02, 1-p=0.98 the probability of non-defective). So in a sample of 1000 bulbs, the mean is 1000*0.02=20 and the standard deviation is sqrt(1000*0.02*0.98)=4.43, implying an expectation of 20+4.43 of defective bulbs (between 15.57 and 24.43 defective bulbs).