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.)

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.)

Transcript text: 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. $\square$ is the Z-score such that the area under the curve to the left is 0.52 . (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Understanding the Problem

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.

Step 2: Finding the Z-score

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:

\[ z \approx 0.05 \]

Step 3: Rounding the Result

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

\[ z \approx 0.05 \]