CA Foundation · Quantitative Aptitude · Theoretical Distributions
The monthly electricity bills of households in a Jaipur colony are normally distributed with mean Rs 1,800 and standard deviation Rs 200. Using the empirical rule (68-95-99.7), what percentage of households have bills between Rs 1,400 and Rs 2,200?
About 95% of households. The range Rs 1,400 to Rs 2,200 is the mean of Rs 1,800 plus or minus two standard deviations of Rs 200, and roughly 95% of a normal distribution lies within two standard deviations of the mean.
- A68%
- B95%Correct
- C99.7%
- D47.5%
Explanation
1,400 = 1,800 - 2(200) and 2,200 = 1,800 + 2(200), so the interval is mean ± 2 SD. About 95% of values lie there. 47.5% is only half of that, covering one side of the mean.
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 made in Ludhiana follow a Poisson distribution at 0.5 defects per metre. What is the mean number of defects in a …
- A fair coin is tossed 3 times and X denotes the number of heads. What is the probability distribution value P(X >= 2)?
- 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…
- For a normal distribution, which statement is correct?
- The monthly electricity bills of households in a Jaipur colony are normally distributed with mean Rs 2,000 and standard deviation Rs 400. Gi…
- If X is normally distributed with mean μ and variance σ², which transformation gives a variable that follows the standard normal distributio…