Question

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.6950.

Answer 1

Since the indicated z-value is to the left of 0, we know already that the z-value is a negative number.

Now, one of the properties of a normal curve is that it is symmetric/balanced. This means that half of the graph has an area of 0.5.

So, if half of the curve is 0.5, then the rest of the shaded area has an area of 0.195.

`0.6950-0.5=0.195`

Using the normal distribution table, let's find the z-value that has an area of 0.195 to the left of the center.

Based on the table, the z-value that has an area of 0.195 from the center is z = 0.51. Since we know that the z-value is negative, then the indicated z-score is -0.51.

The shaded area is to the right of z = -0.51.