Question

The heights of women in The Grand Duchy of Fenwick are normally distributed with a mean of 64 inches and a SD of 2.5 inches. Approximately what percent of women in The Grand Duchy of Fenwick are between 59 and 67.75 inches? 5% 9% 16% 18% 32% 67% 82% 88% 91% 96% (Continued from the previous question) Out of every 10,000 women in The Grand Duchy of Fenwick, approximately how many would you expect to be over 6 feet tall?

Answer 1

Approximately 68% of women in The Grand Duchy of Fenwick are between 59 and 67.75 inches. Out of every 10,000 women, approximately 250 would be expected to be over 6 feet tall.

Step-by-step explanation:

The heights of women in The Grand Duchy of Fenwick are normally distributed with a mean of 64 inches and a standard deviation of 2.5 inches. To find the percentage of women between 59 and 67.75 inches, we can use the empirical rule. The interval from 59 to 67.75 inches is one standard deviation below the mean to one standard deviation above the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation. Therefore, approximately 68% of women in The Grand Duchy of Fenwick are between 59 and 67.75 inches.

For the second part of the question, to estimate the number of women over 6 feet tall, we need to convert the height to inches. 6 feet is equal to 72 inches. The mean height is 64 inches, which means that the difference between 72 inches and 64 inches is 8 inches above the mean. Using the empirical rule, approximately 2.5% of the data falls more than 2 standard deviations above the mean. Therefore, out of every 10,000 women in The Grand Duchy of Fenwick, we would expect approximately 250 to be over 6 feet tall.