Calculating Lowest Passing Grade using Normal Distribution

In this problem, we are looking at a normal distribution of examination grades. We need to find the lowest passing grade, given that the lowest ten percent of students fail.

First, let's write down our known values. The mean, mu, is seventy-four, and the standard deviation, sigma, is seven point nine.

We are told that the bottom ten percent receive an F. This means we are looking for the tenth percentile of the distribution. Let's visualize this on a bell curve.

To find the specific grade, we first need to find the z-score that corresponds to a cumulative area of zero point one zero.

Looking at a standard normal distribution table or using a calculator, the z-score for the tenth percentile is approximately negative one point two eight.

Now, we use the z-score formula to convert this back into an actual grade. The formula is x equals mu plus z times sigma.