3. (2 marks) A city installs 2000 electric lamps for street lighting. These lamp

Question

3. (2 marks) A city installs 2000 electric lamps for street lighting. These lamps have a mean burning life of 1200 hours with a standard deviation of 200 hours. The normal distribution is a close approximation to this case. (a) What is the probability that a lamp will fail in the first 700 burning hours? (b) What is the probability that a lamp will fail between 1050 and 1350 hours? (c) Assuming that lamps fail independent of each other. How many lamps are expected to fail between 1050 and 1350 hours?

Explanation / Answer

Ans:

Normal distribution with mean=1200 and standard deviation=200

a)

z=(700-1200)/200

z=-2.5

P(z<=-2.5)=0.0062

b)

z(1050)=(1050-1200)/200=-0.75

z(1350)=(1350-1200)/200=0.75

P(-0.75<z<0.75)=0.7734-0.2266=0.5468

c)

Number of lamps expected to fail between 1050 and 1350 is=2000*0.5468=1094

d)

P(Z>z)=0.2

P(Z<=z)=1-0.2=0.8

z=normsinv(0.8)=0.84

x=1200+0.84*200

x=1368

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