The height of women in Dewaria follows a normal distribution with mean 160 cm and a standard deviation of 6 cm. In a normal distribution, only 0.0063% of the population is not within 4 standard deviations of the mean. If 5 women are more than 184 cm tall, then which of the following is closest to the number of women who live in Dewaria? A. 16,000 B. 40,000 C. 80,000 D. 100,000 E. 160,000
(E) Since the heights of these women follow a normal distribution, which is symmetric about the mean, there are 5 + 5 = 10 women whose heights are not within 4 standard deviations of the mean. A standard deviation is 6, so 4 standard deviations is 24. There are 5 women below 136 (160 "the mean" minus 24), and 5 above 184 (24 + 160). These 10 women account for 0.0063 % of the total number of women. So if the number of Dewarian women is n, we can write: n × 6.3 / 100000 = 10, so n = (10/6.3) × 100000 = 160000 approximately. The correct answer is choice (E). 
I am not sure how you calculated 10 women. Could you please explain it more?
Thanks.
