Question

A survey found that women's heights are normally distributed with mean 63.8 in. and standard deviation 2.7 in. The survey also found that men's heights are normally distributed with a mean 67.6 in. and standard deviation 2.9. Most of the live characters at an amusement park have height requirements with a minimum of 4 foot 8 in. and a maximum of 6 foot 4 in. Find the percentage of women meeting the height requirement. The percentage of women who meet the height requirement is ___ Round to two decimal places as needed.

Answer 1

The percentage of women who meet the height requirement is approximately 99.86%.

Step-by-step explanation:

To find the percentage of women meeting the height requirement, we need to find the percentage of women whose heights fall within the given range. The height requirement is between 4 foot 8 inches (56 inches) and 6 foot 4 inches (76 inches).

First, we need to convert the height range to z-scores using the formula z = (x - mean) / standard deviation. For the lower threshold, we have z = (56 - 63.8) / 2.7 = -2.96. For the upper threshold, we have z = (76 - 63.8) / 2.7 = 4.52.

Next, we can use a standard normal distribution table or a calculator to find the percentage of women whose heights fall within the z-scores of -2.96 and 4.52. The percentage is approximately 99.86%.