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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

For a distribution of 100 measurements with mean = 60 and standard deviation = 8, approximately how many observations are expected to lie within the range of 44 to 76, using the empirical rule (68-95-99.7)?

Approximately 95 observations are expected within this range. The interval 44 to 76 represents the mean ± 2 standard deviations, and the empirical rule states that 95% of data falls within 2σ of the mean in a normal distribution.

  1. A68
  2. B95Correct
  3. C99.7
  4. D34

Explanation

The range 44 to 76 spans from (60 - 2×8) to (60 + 2×8), which is exactly 2 standard deviations on either side of the mean. According to the empirical rule, approximately 95% of observations lie within 2 standard deviations of the mean. Option 0 (68%) covers only ±1σ, and option 3 (34%) is half of 68%.

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