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CA Foundation · Quantitative Aptitude · Theoretical Distributions

The lifetime of LED bulbs made by a firm in Noida is normally distributed with standard deviation 500 hours. It is known that 15.87% of bulbs last less than 7,500 hours, and P(0 < Z < 1) = 0.3413. What is the mean lifetime of the bulbs?

The mean lifetime is 8,000 hours. A lower-tail area of 0.1587 corresponds to Z = −1. Setting (7,500 − μ)/500 = −1 gives μ = 8,000 hours, since 7,500 lies one standard deviation below the mean.

  1. A7,000 hours
  2. B8,000 hoursCorrect
  3. C7,500 hours
  4. D8,500 hours

Explanation

P(Z < z) = 0.1587 = 0.5 − 0.3413, so z = −1. Then (7,500 − μ)/500 = −1, giving μ = 7,500 + 500 = 8,000. Choosing 7,000 results from using the wrong sign, μ = 7,500 − 500. Check: (7,500 − 8,000)/500 = −1, matching the data.

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