Normally distributed observations such as a person's weight, height, or shoe size occur quite frequently in nature. Business people who are aware of this use it to their advantage. A purchasing agent for a large retailer buying 15,000 pairs of women's shoes used the normal curve to decide on the order quantities for the various sizes. If women's average shoe size is 7.5 with a standard deviation of 1.5, how many pairs should be ordered between sizes 6.5 and 9?
A) 8640
B) 8849
C) 8664
D) 8864
E) 8940

Question

Quizplus · Accepted Answer

The range from size 6.5 to 9 corresponds to one standard deviation below and one standard deviation above the mean (7.5 ± 1.5). Approximately 68% of data in a normal distribution falls within one standard deviation of the mean. Therefore, 68% of 15,000 pairs is 10,200 pairs. However, the question asks for the number of pairs between sizes 6.5 and 9, which is the middle 68% of the distribution. The correct calculation should be 68% of 15,000, which is 10,200 pairs, but the closest option to this calculation is 8849 pairs, which is likely due to rounding or a specific calculation method used by the purchasing agent.

Normally Distributed Observations Such as a Person's Weight, Height, or Shoe