A trouser manufacturer has an order for 800,000 men's trousers in a normal distribution of waist sizes 28, 30, 32, 34, 36, 38, 40, 42, and 44 with a mean of 34 and a sample standard deviation of 1.8. Find the number of trousers to be made of each waist size.
A) 568,000 trousers of size 34; 168,000 of sizes 32 and 36; 33,600 of sizes 30 and 38; 30,400 of sizes 28, 40, 42 and 44
B) 544,000 trousers of size 34; 216,000 of sizes 32 and 36; 37,600 of sizes 30 and 38; 2,400 of sizes 28, 40, 42 and 44
C) 512,000 trousers of size 34; 248,000 of sizes 32 and 36; 35,200 of sizes 30 and 38; 4,800 of sizes 28, 40, 42 and 44
D) 600,000 trousers of size 34; 136,000 of sizes 32 and 36; 51,200 of sizes 30 and 38; 12,800 of sizes 28, 40, 42 and 44
E) 440,000 trousers of size 34; 280,000 of sizes 32 and 36; 42,400 of sizes 30 and 38; 37,600 of sizes 28, 40, 42 and 44

Question

Quizplus · Accepted Answer

To determine the correct distribution of trousers, we use the properties of a normal distribution. The mean is given as 34, and the standard deviation is 1.8. In a normal distribution, about 68% of values fall within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations. Given the sizes and the distribution, we can infer that the majority of trousers will be around the mean size of 34, with decreasing quantities for sizes further from the mean. However, without specific percentages for each size, we cannot accurately calculate the exact number of trousers for each size. Choice B is selected based on an understanding of normal distribution properties, but the exact numbers provided in the choices cannot be directly derived from the information given without additional statistical data such as z-scores or the exact distribution percentages for each size.

A Trouser Manufacturer Has an Order for 800,000 Men's Trousers