Assume the heights of children are normally distributed with the mean and standard deviation you calculated in the last question. What percent of children have heights between 61.6 cm and 74.9 cm ?

To find the percentage of children with heights between 61.6 cm and 74.9 cm in a normal distribution, you can use the z-score formula: \( z = \frac{(X - \mu)}{\sigma} \). First, you'll need the mean (μ) and standard deviation (σ) of the distribution. Once you have the z-scores for both heights, you can consult a standard normal distribution table or use a calculator to find the corresponding percentiles. The final step is subtracting the lower percentile from the upper percentile to get the percentage of children within that height range. Calculating z-scores not only allows for understanding distribution but also connects to interesting data applications! For instance, educational institutions often use these techniques to analyze students’ physical growth patterns, helping ensure they meet health standards. It’s fascinating to see how that data can influence sports programs or nutrition initiatives aimed at improving children's health and athletic performance!