Assume that 150 scores are normally distributed with a mean of 92 and a standards deviation of 11.5

WHat percentage of the scores fall between 69 and 115?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z scores.

To find the percentage of scores that fall between 69 and 115, we'll need to use the properties of the standard normal distribution.

First, we need to convert the given values into z-scores. The formula for calculating the z-score is:

z = (x - μ) / σ

Where:
x = the value we're interested in (either 69 or 115 in this case)
μ = the mean of the distribution (92 in this case)
σ = the standard deviation of the distribution (11.5 in this case)

Let's calculate the z-scores for both 69 and 115:

z1 = (69 - 92) / 11.5
z2 = (115 - 92) / 11.5

Now, we need to find the area (percentage) under the standard normal curve between these two z-scores. We can do this by using a normal distribution table or a calculator.

If we assume the table or calculator gives us the area between z1 and z2 as A, then the percentage of scores that fall between 69 and 115 is approximately A * 100%.

So, the next step is to find the area (A) between the z-scores 69 and 115 using the table or calculator. This will give you the percentage of scores that fall within that range.