Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?Question 9Select one:a.0.0145b.0.0012c.0.0000

Break Down the Problem

1. The problem requires us to find the value of $Z$ such that the area to the right of $Z$ in the standard normal distribution is 0.5.
2. We know that in a standard normal distribution, the total area under the curve is 1, and the area to the left of $Z$ plus the area to the right of $Z$ equals 1.

Relevant Concepts

1. For a standard normal distribution $Z$, the area to the left of $Z$ can be represented as $P(Z \leq z)$.
2. Therefore, if the area to the right is 0.5, we have: $P(Z \leq z) = 1 - P(Z > z) = 1 - 0.5 = 0.5$

Analysis and Detail

1. To find $Z$ where $P(Z \leq z) = 0.5$, we can refer to the standard normal distribution table (Z-table).
2. The Z-table shows values of $z$ for corresponding areas. The area of 0.5 corresponds to $Z = 0$ because it is the mean of the standard normal distribution.

Verify and Summarize

1. We have identified that when the area to the right of $Z$ is 0.5, the area to the left is also 0.5.
2. Since $Z = 0$ is the balance point of the standard normal curve, the calculations are verified.

Final Answer

The value of $Z$ such that the area to the right is 0.5 is: $\boxed{0}$