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 ?
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To find the percentage of children with heights between 61.6 cm and 74.9 cm, you would use the properties of the normal distribution. First, convert the heights to z-scores using the formula: \( z = \frac{(X - \mu)}{\sigma} \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation. After calculating the z-scores for both heights, you'd look up these z-scores in a standard normal distribution table or use a statistical calculator to find the corresponding probabilities. By subtracting the lower probability from the upper probability, you can determine the percentage of children within that height range. Don't forget that the total area under the normal distribution curve equals 100%, so whatever value you find can be interpreted as the percentage of children within that height range!
