A data distribution has a mean of 12 and a standard deviation of 3. The distribution is bell shaped. Estimate the proportion that falls between 6 and 18
To estimate the proportion that falls between 6 and 18, we can use the standard normal distribution.
First, we calculate the z-scores for the lower and upper values:
Lower z-score = (6 - 12) / 3 = -2
Upper z-score = (18 - 12) / 3 = 2
Next, we find the area under the standard normal distribution curve between these z-scores. We can use a standard normal distribution table or a calculator to find the area.
From a standard normal distribution table or calculator, we find that the area to the left of -2 is approximately 0.0228 and the area to the left of 2 is approximately 0.9772.
To estimate the proportion between -2 and 2, we subtract the smaller area from the larger area:
0.9772 - 0.0228 = 0.9544
Therefore, approximately 95.44% of the data falls between 6 and 18.