The Classical Consultant Company provides forecasting research for clients such as a group of five doctors associated with a new hospital health-maintenance program.The company has been asked to forecast the number of patients requesting blood analysis per week.The past weekly average is 38 and,for the trend,is 2 per week.This week's demand was 42 blood tests.How many patients will come next week? (Suppose = 0.10 and = 0.30. )
A)fewer than or equal to 39
B)greater than 39 but fewer than or equal to 41
C)greater than 41 but fewer than or equal to 43
D)greater than 43

Question

Quizplus · Accepted Answer

The trend is given as 2 per week, so we can add this to the past weekly average of 38 to get an expected demand of 40 for next week.

To account for random fluctuations, we can use the formula:

Expected Demand ± Z-score*Standard Error

where the Z-score depends on our chosen level of confidence and the standard error takes into account the variability in the data.

With = 0.10 and = 0.30, we can calculate the standard error as:

Standard Error = sqrt( (1-0.30)/5 ) ≈ 0.346

Using = 0.10, the corresponding Z-score is -1.28. Thus:

Expected Demand - Z-score*Standard Error = 40 - (-1.28)*0.346 ≈ 40.44

Using = 0.30, the corresponding Z-score is 0.52. Thus:

Expected Demand + Z-score*Standard Error = 40 + 0.52*0.346 ≈ 40.17

Therefore, the range of likely demand for next week is between 40.17 and 40.44. This includes option C, which is the best choice.

The Classical Consultant Company Provides Forecasting Research for Clients Such