CA Foundation · Quantitative Aptitude · Theoretical Distributions
The daily sales of a Kolkata store are normally distributed. It is known that 15.87% of days have sales above ₹68,000 and, by symmetry, 15.87% of days have sales below ₹52,000. Given that P(Z > 1) = 0.1587, what are the mean and standard deviation of daily sales?
The mean is ₹60,000 and the standard deviation is ₹8,000. Since 15.87% lies beyond one standard deviation on each side, the two limits are mean plus SD and mean minus SD, so the mean is their midpoint and the SD is half their gap.
- AMean ₹60,000; SD ₹8,000Correct
- BMean ₹60,000; SD ₹4,000
- CMean ₹64,000; SD ₹4,000
- DMean ₹60,000; SD ₹16,000
Explanation
Z = 1 is the point above which 15.87% lies, so mean + SD = 68,000 and mean − SD = 52,000. Adding gives mean = 60,000 and subtracting gives 2 SD = 16,000, so SD = 8,000. The option with SD 4,000 treats the gap of 8,000 from the mean as 2 SD, and 16,000 uses the full gap as one SD.
Did you get it right without looking?
One question tells you little. A timed set on Theoretical Distributions shows your real accuracy, how long you take and where you lose marks.
More Theoretical Distributions questions
- Defects in a roll of cloth produced by a Ludhiana mill follow a Poisson distribution. It is known that P(X=1) = P(X=2) for the number of def…
- A continuous random variable X follows a normal distribution with mean 50 and standard deviation 10. If Z represents the standardised normal…
- A salesperson in Jaipur closes a sale with probability 0.2 on each independent call. In 5 calls, what is the probability of at least one sal…
- The monthly electricity consumption of households in a Nagpur colony is normally distributed with mean 220 units and standard deviation 40 u…
- If X follows a binomial distribution with n = 6 and p = 1/2, which statement about the distribution is correct?
- A binomial distribution has n = 100 and p = 0.02. Which Poisson distribution gives the best approximation to it?