CA Foundation · Quantitative Aptitude · Theoretical Distributions
The lifetimes of LED bulbs made by a firm are normally distributed with mean 1,000 hours and standard deviation 100 hours. If P(0 < Z < 1) = 0.3413, what proportion of bulbs last more than 1,100 hours?
The proportion of bulbs lasting more than 1,100 hours is 0.1587. The standardised value is 1, and the upper tail beyond Z equal to 1 is 0.5 minus 0.3413, which equals 0.1587.
- A0.3413
- B0.6826
- C0.1587Correct
- D0.8413
Explanation
Z = (1100 − 1000)/100 = 1. P(Z > 1) = 0.5 − P(0 < Z < 1) = 0.5 − 0.3413 = 0.1587. The option 0.3413 forgets to subtract from 0.5, and 0.8413 is P(Z < 1).
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