CA Foundation · Quantitative Aptitude · Theoretical Distributions
The daily sales of a Jaipur sweet shop are normally distributed with mean ₹8,000 and standard deviation ₹1,000. Given P(0 < Z < 2) = 0.4772, what is the probability that sales on a day are less than ₹6,000?
The probability is 0.0228. Sales of ₹6,000 correspond to Z = -2, and the lower tail area is 0.5 minus 0.4772, which equals 0.0228. Doubling it to 0.0456 would wrongly include the upper tail as well.
- A0.0228Correct
- B0.0456
- C0.4772
- D0.9772
Explanation
Z = (6,000 - 8,000)/1,000 = -2. P(Z < -2) = 0.5 - P(0 < Z < 2) = 0.5 - 0.4772 = 0.0228. The value 0.0456 doubles this by counting both tails, which is wrong since only the lower tail is asked.
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