If the standard deviation of demand is 100 units and the average demand is 1000 units, then we can be 95% confident that actual sales will be 1000 units plus or minus about:
A) 100 units
B) 150 units
C) 200 units
D) 300 units
E) 400 units

Question

Quizplus · Accepted Answer

To calculate the range of actual sales we use the formula: 
Range = z * (standard deviation /sqrt(n))
where z is the z-score from the standard normal distribution for the desired confidence level (in this case, 95%, so z=1.96), and n is the sample size (which is not given, so we assume it is large enough for us to use the population standard deviation).

Plugging in the given values, we get:
Range = 1.96 * (100 / sqrt(n))
To solve for n, we rearrange the formula and square both sides:
(n * Range^2) / (1.96^2 * 100^2) = 1 
(n * Range^2) / 38416 = 1 
n = 38416 / Range^2

Since we want the range to be within 100 units of the average demand (1000 units), we set the Range equal to 100:
n = 38416 / 100^2 = 384.16

Since we can't have a fraction of a unit, we round up to the nearest whole number:
n = 385

So our final range is:
Range = 1.96 * (100 / sqrt(385)) = 20.07

Therefore, we can be 95% confident that actual sales will be 1000 units plus or minus about 20 units, which is closest to answer choice C (200 units).

If the Standard Deviation of Demand Is 100 Units and the Average