The lifetime of the LCD television sets are approximately distributed as normal

Question

The lifetime of the LCD television sets are approximately distributed as normal variate. There are 10000 LCD television of a particular brand have been installed by an advertising company, of which 5% of the television works more than 1500 hours and 4 % of the television sets fail in less than 600 hours. How many television sets might be expected to fail in

(i) in the first 800 hours?

(ii) between 800 and 1200 hours?

(iii) After how many hours would you expect

(a) of sets fail?

(b) 10% of the sets to be still working?

Explanation / Answer

here let mean =z and std deviaitron =y

for top 5 percentile z=1.645

hence x+1.645y =1500 ............(1)

for bottom 4 % ; z =-1.751

hence x-1.751y=600............(2)

solving above equation

x=1064.03=mean

y=265.05 =std deviation

(i) P(X<800)=P(Z<(800-1064.03)/265.05)=P(Z<-0.9961)=0.1596

hence television sets might be expected to fail=np=10000*0.1596=1596

(ii) P(800<X<1200)=P(-0.9961<Z<0.513)=06960-0.1596=0.5364

hence television sets might be expected to fail=np=10000*0.5364=5364

b)for top 10% , z=1.2816

hence number of hours 1064.03+1.2816*265.05 =1403.705 hours

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