Questions: Find the Z-score such that the area under the standard normal curve to the left is 0.52. Click the icon to view a table of areas under the normal curve. The Z-score such that the area under the curve to the left is 0.52. (Round to two decimal places as needed.)

Solution Steps

We need to find the Z-score such that the area under the standard normal curve to the left is $0.52$. This means we are looking for a value $z$ such that:

$$P(Z < z) = 0.52$$

where $Z$ is a standard normal random variable.

To find the Z-score corresponding to the cumulative probability of $0.52$, we can use the inverse of the cumulative distribution function (CDF) for the standard normal distribution. This is denoted as:

$$z = \Phi^{-1}(0.52)$$

Using statistical tables or computational methods, we find:

$$z \approx 0.05$$

The Z-score calculated is $0.05$. Since the problem requires rounding to two decimal places, we have:

$$z \approx 0.05$$

Final Answer