Finding a Value in a Normal Distribution

In this problem, we are given a normal distribution and asked to find a specific x value based on the area above it.

Let's list the known parameters: the mean mu is two hundred, and the standard deviation sigma is ten.

We are looking for an x value such that thirty-five percent of the area is above it. This means the area to the right of x is zero point three five.

Since standard normal distribution tables usually show the area to the left, we calculate that as one minus zero point three five, which equals zero point six five.

Let's visualize this on a normal distribution curve.

Now we need to find the z-score that corresponds to a cumulative area of zero point six five. Using a standard normal table or calculator, we find z is approximately zero point three eight five.