Probability Puzzle
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The lifetime of a color TV picture tube is normally distributed, with a mean of 8 years and a std. dev. of 2 years.
(i) What is the probability that a picture tube will last more than 10 years?
(ii) If the firm guarantees the picture tube for 4 years, what percentage of the tubes sold will have to be replaced?
(i)The distribution can be converted into a standard normal distribution, with mean 0 & variance 1.
So, P(t>10)=1-P(t=<10)
Converting to normal standard deviation, it comes out as
P(x>1)=1-P(x=<1)=1-0.84134=0.15866
(ii) Proceeding in similar fashion, the probability of tubes with life less than 4 years is the solution. Converting it to normal standard distribution, it comes down to:
P(x<-2)=P(x>2)=1-P(x=<2)=1-0.97725=0.02275
=2.275%
P.S.:
1. You will need normal distribution tables.
2. A normal distribution with mean m & standard deviation a is equivalent to standard normal distribution (x-m)/a
Your Answer
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