The life expectancy of computer terminals is normally distributed with a mean of

Question

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation of 0.5 year (or 6 months). a. What percentage of terminals will last less than 4 years? b. What is the probability that a randomly selected terminal will last more than 5 years? c. What percentage of terminals will last between 3 and 4.5 years? d. If the manufacturer guarantees the terminals for 3 years (and will replace them if they malfunc what percentage of terminals will be replaced within 3 years of warranty?

Explanation / Answer

1) Since mean = 4 years, exactly 50% will last less than 4 years.

2) Z = x-mean/sigma = (5-4)/0.5 = 2

P(Z>2) = 0.02275 from normal tables.

3) Required probability = P(-2<z<1) = 0.841345 - 0.02275 = 0.818595=81.85%

4) Required probability = P(z<-2) =  0.02275= 2.275%

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