CA Foundation · Quantitative Aptitude · Theoretical Distributions
The daily sales of a shop in Indore are normally distributed with mean Rs 5,000 and standard deviation Rs 500. Given that the area between Z = 0 and Z = 1 is 0.3413 and between Z = 0 and Z = 2 is 0.4772, what is the probability that daily sales lie between Rs 4,500 and Rs 6,000?
The probability is 0.8185. Sales of Rs 4,500 correspond to Z = -1 and Rs 6,000 to Z = 2. Adding the areas on either side of the mean, 0.3413 and 0.4772, gives 0.8185, because the limits lie on opposite sides of the mean.
- A0.8185Correct
- B0.6826
- C0.9544
- D0.1359
Explanation
Z for 4,500 = (4,500 - 5,000)/500 = -1; Z for 6,000 = (6,000 - 5,000)/500 = 2. Probability = 0.3413 + 0.4772 = 0.8185. The value 0.6826 would be the area between Z = -1 and 1, and 0.9544 between -2 and 2, both using wrong limits.
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