The height of women in Dewaria follows a normal distribution with mean 160 cm and 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, approximately how many women live in Dewaria?
the answer doesn't add up.... 0.0063 of 160,000 is actually 1008 not 10 as suggested in the answer explanation, can you help ?
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)/100,000 = 10, so n = (10/6.3) × 100,000 = 160,000 approximately.
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