Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated
Approximately mean ±2Z or ±2SD
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that applies to a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations of the mean.
To calculate the approximate range for 95% of female heights using the empirical rule, we need to know the mean and standard deviation of the heights dataset. Let's assume we have a dataset of female heights with a mean of 64 inches and a standard deviation of 3 inches.
Step 1: Calculate one standard deviation.
One standard deviation is equal to the mean plus or minus the standard deviation. In this case, it would be 64 + 3 = 67 inches and 64 - 3 = 61 inches.
Step 2: Calculate two standard deviations (95% range).
Two standard deviations would be 67 + (2 * 3) = 67 + 6 = 73 inches and 61 - (2 * 3) = 61 - 6 = 55 inches.
Therefore, based on the empirical rule, approximately 95% of female heights should fall between 55 and 73 inches.