CA Foundation · Quantitative Aptitude · Theoretical Distributions
The daily sales of a Lucknow sweet shop are normally distributed with mean Rs 20,000 and standard deviation Rs 4,000. Given the area from Z = 0 to Z = 0.5 is 0.1915 and from Z = 0 to Z = 1 is 0.3413, what is the probability that sales on a day lie between Rs 18,000 and Rs 24,000?
The probability is 0.5328. The limits convert to Z = -0.5 and Z = 1, which lie on opposite sides of the mean, so the areas add: 0.1915 + 0.3413 = 0.5328.
- A0.1498
- B0.5328Correct
- C0.3413
- D0.1915
Explanation
Z for 18,000 = -0.5 and for 24,000 = +1. The probability is 0.1915 + 0.3413 = 0.5328. Option 0.1498 wrongly subtracts the two areas, treating the values as on the same side of the mean.
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