The mean (μ) of the scale is 98 and the standard deviation (σ) is 13. Assuming that the scores are normally distributed, what is the PROBABILITY that a score falls below 88?

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 score.

What is the approximate probability that x will differ from μ by more than 0.8?

To find the probability that a score falls below a certain value, we can use z-scores and the standard normal distribution.

The z-score measures the number of standard deviations a value is from the mean. It is calculated using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability of a score falling below 88.

First, let's calculate the z-score for 88 using the given mean and standard deviation:

z = (88 - 98) / 13
z = -10 / 13
z ≈ -0.7692

Now, we can find the probability using a standard normal distribution table (also known as a z-table) or using a calculator.

Using a standard normal distribution table, we look up the z-score of -0.7692 and find the corresponding probability. Let's assume the probability is P.

Therefore, the probability that a score falls below 88 is P.