CA Foundation · Quantitative Aptitude · Theoretical Distributions
The monthly electricity consumption of households in a Jaipur colony is normally distributed with mean 200 units and standard deviation 40 units. Using the standard result that about 95% of values lie within 1.96 standard deviations of the mean, between which limits do the middle 95% of households' consumption lie?
The middle 95% of households lie between 121.6 and 278.4 units. This comes from mean plus or minus 1.96 times the standard deviation, that is 200 plus or minus 78.4, since 1.96 multiplied by 40 equals 78.4.
- A120 and 280 units
- B80 and 320 units
- C160 and 240 units
- D121.6 and 278.4 unitsCorrect
Explanation
Limits = mean ± 1.96 × SD = 200 ± 1.96 × 40 = 200 ± 78.4, giving 121.6 and 278.4 units. The option 120 and 280 uses 2 SD, which is the approximate rounding and not the stated 1.96 value. The option 160 and 240 uses only 1 SD.
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