Defective rate. A machine that produces a special type of transistor (a componen

Question

Defective rate. A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others. (a) What is the probability that the 10th transistor produced is the first with a defect? (b) What is the probability that the machine produces no defective transistors in a batch of 100? (c) On average, how many transistors would you expect to be produced before the first with a defect? What is the standard deviation? (d) Another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. On average how many transistors would you expect to be produced with this machine before the first with a defect? What is the standard deviation? (e) Based on your answers to parts (c) and (d), how does increasing the probability of an event affect the mean and standard deviation of the wait time until success?

Explanation / Answer

a) probabilty that 10th one is first defective =P(first 9 non defective)*10th is first defectvie =)=(1-0.02)9*0.02=0.016675

b)probabilty that no defective in a batch of 100 =(1-0.02)100 =0.1326196

c)from geomteric distribution average number =1/p=1/0.02=50

std deviation =((1-p)/p2)1/2 =49.4975

d) p=0.05

average=1/p=1/0.05=20

std deviaiton=19.49

e)increasing probability , reduce mean and std deviaiton

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