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. Complete parts a through c below.

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

To find the percentage of women meeting the height requirement, calculate the z-scores for the height limits and find the area under the curve between these z-scores using a standard normal distribution table or calculator.

Step-by-step explanation:

To find the percentage of women meeting the height requirement, we need to find the proportion of women whose heights fall within the range of 4 foot 8 inches to 6 foot 4 inches. We can convert these heights to inches, which gives us a range of 56 to 76 inches.

Next, we can calculate the z-scores for these height limits using the formula z = (x - μ) / σ, where x is the height, μ is the mean height, and σ is the standard deviation. For the lower limit, z = (56 - 63.8) / 2.7 = -2.96. For the upper limit, z = (76 - 63.8) / 2.7 = 4.49.

Using a standard normal distribution table or a calculator, we can find the area under the curve between these two z-scores. This represents the percentage of women meeting the height requirement. The percentage is approximately 99.91%.