Questions: For the standard normal variable Z, find (z0.44), the value that divides the area under the density curve into 0.56 to the left and 0.44 to the right. (z0.44=) (Round the answer to 2 decimal places)

Solution Steps

We need to find \( z_{0.44} \), which is the z-score that divides the area under the standard normal distribution such that 0.56 of the area is to the left and 0.44 is to the right. This means we are looking for the z-score corresponding to a cumulative probability of 0.56.

The cumulative distribution function (CDF) for the standard normal distribution is denoted as \( \Phi(z) \). We need to find \( z \) such that:

\[ \Phi(z) = 0.56 \]

Using the properties of the standard normal distribution, we know that:

\[ \Phi(-\infty) = 0 \quad \text{and} \quad \Phi(\infty) = 1 \]

Thus, the probability \( P \) for the range from \( -\infty \) to \( \infty \) is:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(-\infty) = 1.0 \]

The output indicates that the z-score corresponding to the cumulative probability of 0.56 is \( z_{0.44} = \infty \). This suggests that there is no finite z-score that satisfies the condition of having 0.44 of the area to the right.

Final Answer