CA Foundation · Quantitative Aptitude · Theoretical Distributions
A factory produces ball bearings with a mean diameter of 8 mm and standard deviation of 0.2 mm, normally distributed. If the specification allows diameters between 7.6 mm and 8.4 mm, what proportion of bearings lie within specifications?
Approximately 95.45% of bearings meet specifications. The limits 7.6 and 8.4 represent μ ± 2σ, and the empirical rule states that 95.45% of normally distributed data falls within this range.
- A68.27%
- B95.45%Correct
- C99.73%
- D78.12%
Explanation
The lower limit 7.6 = 8 - 2(0.2), representing mean minus 2 standard deviations. The upper limit 8.4 = 8 + 2(0.2), representing mean plus 2 standard deviations. From the empirical rule, approximately 95.45% of data falls within 2 standard deviations of the mean. Option 68.27% is for ±1σ; 99.73% is for ±3σ.
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