Question

The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches.

Find the interquartile range for the height of women aged 20-29.

Answer 1

To find the interquartile range for the height of women aged 20-29, we can use the properties of the normal distribution to find the quartiles.

Step-by-step explanation:

To find the interquartile range for the height of women aged 20-29, we first need to find the quartiles of the height distribution. The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1).

Given that the heights of women aged 20-29 are approximately normally distributed with a mean of 64 inches and a standard deviation of 2.7 inches, we can use the properties of the normal distribution to find the quartiles.

The lower quartile (Q1) is given by the formula Q1 = mean - (1.349 * standard deviation) and the upper quartile (Q3) is given by the formula Q3 = mean + (1.349 * standard deviation). Substituting the given values, we get Q1 = 64 - (1.349 * 2.7) and Q3 = 64 + (1.349 * 2.7).

Finally, to find the interquartile range, we subtract Q1 from Q3: Interquartile range = Q3 - Q1.