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CA Foundation · Quantitative Aptitude · Theoretical Distributions

The lifetimes of LED bulbs made by a Pune firm are normally distributed with mean 12,000 hours. It is known that 15.87% of bulbs last more than 13,500 hours. Using the fact that P(Z > 1) = 0.1587, what is the standard deviation of the lifetimes?

The standard deviation is 1,500 hours. A 15.87% upper tail corresponds to Z = 1, so 13,500 lies exactly one standard deviation above the mean of 12,000, giving SD = 1,500.

  1. A750 hours
  2. B3,000 hours
  3. C1,500 hoursCorrect
  4. D1,350 hours

Explanation

P(Z > 1) = 0.1587 means 13,500 is one SD above the mean. So SD = 13,500 - 12,000 = 1,500. Option 750 wrongly assumes 13,500 is two SDs above the mean.

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