An analyst determines that approximately 99 percent of the observations of daily sales for a company are within the intervals from $230,000 to $480,000 and that daily sales for the company are normally distributed. The standard deviation of daily sales for the company is closest to:
A. 41,667
B. 62,500
C. 83,333作者: dece2011 时间: 2011-7-11 18:38
That is the correct answer, but I am interested in seeing how people arrived to that answer.作者: mnieman 时间: 2011-7-11 18:38
i get 48,449
125,000 / 2.58
...作者: thisisbrianly 时间: 2011-7-11 18:38
Shouldn't the 99% Confidence Interval be 2.58 instead of using Chebyshev's inequality...which gives 3?作者: suyash1989 时间: 2011-7-11 18:38
48,449 is technically correct. However, the 41,667 is obtained using the approximate rule that 99% of observations will fall within +/- 3 standard deviations of the mean.
got ya - using 3 instead of 2.58作者: Siddimaula 时间: 2011-7-11 18:38
I don't get it.
125,000/2.576 = Standard Error
$48,524.84 = SE
Standard Deviation/Sqrt(n) = $48,524.84
Given 62,500 and 83,333 as standard deviations...
A makes no sense.
B. (62500/48524)^2=n n=1.659
C. (83333/48524)^2=n n=2.9493
Probably C neh?作者: ajpheif16 时间: 2011-7-11 18:38
technically for z score 99.7% = 3 but in this case its using 3 for 99% instead of 2.58
So 230+480 / 2 = 355 = mean
355 +- 3(X) = 480
480 - 355 = 125
125/3 = 41667
Edited 1 time(s). Last edit at Tuesday, June 2, 2009 at 12:33PM by chung.da.neu.作者: ramdabom 时间: 2011-7-11 18:38
sujian Wrote:
-------------------------------------------------------
> Nope, still don't get it, why does 125k/3 =
> standard deviation instead of standard error?
Because we are talking about the population distribution, not a sample statistic.作者: pogo 时间: 2011-7-11 18:38
I'm not sure if my method is right, I just remember estimating it from college stats class.
We know that in a normal distribution:
68% is +/- one standard deviation
95% is +/- two standard deviations
99% is +/- three standard deviations
so at 99% there is a range of six standard deviations
480,000-230,000 = 250,000
250,000/6 = 41,666作者: trogulj 时间: 2011-7-11 18:38
Interesting way of looking at the problem using Chebyshev's inequality. Here is the answer explanation as per CFAI.
"Given that the sales are normally distributed, the mean is centered in the interval.
Mean = (230+480)/2 = 355. 99% of observations under a normal distribution will be +/- 3 std devs. Thus (355-230)/3 = 41,667. It is also the case that (480-355)/3 = 41,667."
