Assuming that the distribution is normal for weight relative to the ideal and 99% of the male participants scored between (–53.68, 64.64), where did 95% of the values for weight relative to the ideal lie? R
You can plug in your data and play around with it at
http://davidmlane.com/hyperstat/z_table.html
To find the range where 95% of the values for weight relative to the ideal lie, we can use the concept of confidence intervals.
In a normal distribution, 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean on both sides. Since the given range (-53.68, 64.64) represents the 99% confidence interval, we can calculate the standard deviation using the formula:
(64.64 - (-53.68)) / (2 * 1.96) = 118.32 / 3.92 ≈ 30.17
Now, to find the range for the 95% confidence interval, we multiply the standard deviation by 1.96:
1.96 * 30.17 = 59.11
Therefore, the range for 95% of the values for weight relative to the ideal would be approximately (-59.11, 59.11).