CA Foundation · Quantitative Aptitude · Theoretical Distributions
The daily sales of a Kolkata shop are normally distributed. It is known that 6.68% of days have sales above Rs 26,000 and the mean is Rs 20,000. Given that P(0 < Z < 1.5) = 0.4332, what is the standard deviation of daily sales?
The standard deviation is Rs 4,000. A 6.68% upper tail corresponds to Z = 1.5, so Rs 6,000 above the mean equals 1.5 standard deviations, giving 6,000 divided by 1.5, which is Rs 4,000.
- ARs 6,000
- BRs 4,000Correct
- CRs 3,000
- DRs 2,000
Explanation
Upper tail 0.0668 means area from 0 to Z is 0.5 - 0.0668 = 0.4332, so Z = 1.5. Then (26,000 - 20,000)/σ = 1.5, giving σ = 6,000/1.5 = 4,000. Check: 20,000 + 1.5(4,000) = 26,000. Rs 6,000 wrongly uses Z = 1.
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
- A binomial variable X has n = 8 and p = 0.5. Which statement about its distribution is correct, and what is P(X = 4)?
- The marks of students in a test are normally distributed with mean 60 and standard deviation 5. Given that the area under the standard norma…
- A binomial distribution has mean 12 and variance 9. What are the values of n and p?
- The monthly electricity bills of households in a Nagpur colony are normally distributed with mean ₹1,200 and standard deviation ₹200. Using …
- A fair coin is tossed 8 times. What is the probability of getting exactly 3 heads?
- For a Poisson distribution, which of the following statements is correct?