A variable is normally distributed with a mean of 100 and a standard deviation of 10. What percentage of observations of the variable lie between 106 and 110?

To answer this question, we need to use the properties of the standard normal distribution.

Step 1: Standardize the values First, we need to convert the values 106 and 110 into z-scores. The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation.

For 106: Z = (106 - 100) / 10 = 0.6

For 110: Z = (110 - 100) / 10 = 1

Step 2: Look up the z-scores in the standard normal distribution table Next, we look up these z-scores in the standard normal distribution table (or use a calculator or software that can do this).

The value for Z=0.6 is approximately 0.7257, which means that approximately 72.57% of the data falls below a score of 106.

The value for Z=1 is approximately 0.8413, which means that approximately 84.13% of the data falls below a score of 110.

Step 3: Find the percentage of observations between 106 and 110 Finally, to find the percentage of observations that lie between 106 and 110, we subtract the percentage of observations below 106 from the percentage of observations below 110.

So, 0.8413 - 0.7257 = 0.1156

Therefore, approximately 11.56% of observations lie between 106 and 110.