Question

Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, answer the following questions. What percentages of women are taller than 65 inches? What percentages of women are shorter than 65 inches? What percentages of women are between 62.5 inches and 67.5 inches? What percentages of women are between 60 inches and 70 inches?

Answer 1

The percentages of women falling into different height ranges are calculated using the mean and standard deviation of college women's heights.

Step-by-step explanation:

The percentages of women who fall into different height ranges are as follows:

a. The percentage of heights that are from 67.95-71.95 inches is ___%.
b. The percentage of heights that are from 67.95-73.95 inches is ___%.
c. The percentage of heights that are more than 65.95 inches is ___%.
d. The number of players in the sample who are between 61.95 and 71.95 inches tall is ___.

The heights of college women are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches.

Answer 2

In a normal distribution with a mean of 65 inches and a standard deviation of 2.5 inches, 50% of college women are taller than 65 inches, 50% are shorter, about 68.26% are between 62.5 and 67.5 inches, and about 95.44% are between 60 and 70 inches.

Step-by-step explanation:

Assuming that the heights of college women are normally distributed with a mean (μ) of 65 inches and a standard deviation (σ) of 2.5 inches, we can answer the following questions using properties of the normal distribution:

1. The percentage of women who are taller than 65 inches is 50%. This is because 65 inches is the mean of the distribution, so half of the values lie above it.

2. The percentage of women who are shorter than 65 inches is also 50%, for the same reason that 65 inches is the mean.

3. To find the percentages of women between 62.5 inches and 67.5 inches, we note that this range is exactly one standard deviation below and above the mean. Approximately 68.26% of the distribution lies within +/-1 standard deviation from the mean in a normal distribution.

4. For women between 60 inches (2 standard deviations below the mean) and 70 inches (2 standard deviations above the mean), approximately 95.44% of the distribution is contained within this range, by the empirical rule.

The heights represent continuous quantitative data.