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
a?
That is the correct answer, but I am interested in seeing how people arrived to that answer.
i get 48,449 125,000 / 2.58 …
Shouldn’t the 99% Confidence Interval be 2.58 instead of using Chebyshev’s inequality…which gives 3?
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. Mean = 355000 3 std. dev. = (480000 - 355000) = 125000 1 std. dev = 41,666.67
If you use 2.58 A is still the closest answer.
I get a standard deviation of 48,450 so closest is 41,667 - answer a. Mean = 355,000 Mean + 2.58 x sd = 480,000 sd = 48,450 Can somebody correct why I am not getting 41,667?
got ya - using 3 instead of 2.58
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?
Nope, still don’t get it, why does 125k/3 = standard deviation instead of standard error?
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
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.
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
wyantjs Wrote: ------------------------------------------------------- > 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. There is no standard error since we are dealing with a population. You must have the same size, n, to calculate a standard error. lincfucious shows a nice way of estimating the answer (the answer is, in fact, an approximation not an exact figure.).
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.”
Chebyshev’s inequality. Is that 3 stds make 89% of the observations. The rule here is based on that we are given a normal populations distribution. Look up the emprical rule, that is what we are using here.