Find the Z-value with an area of 0.7134 under the standard normal curve to its right.

To find the Z-value with an area of 0.7134 under the standard normal curve to its right, you need to use the Z-table or a standard normal distribution calculator.

However, the Z-table typically gives the area to the left of the Z-value. So, you need to convert the area to the left first.

Since the total area under the curve is 1, the area to the left of the Z-value is 1 - 0.7134 = 0.2866.

Now, you can look up this value in the Z-table or use a standard normal distribution calculator to find the corresponding Z-value.

The Z-value that corresponds to an area of 0.2866 to the left under the standard normal curve is approximately -0.56.

So, the Z-value with an area of 0.7134 to its right is approximately -0.56.