Suppose a normal distribution is shown with a mean of $\mu =0$ and a standard deviation of $\sigma =1$. If the shaded area to the left of the indicated point is $0.8413$, what is the z-score corresponding to the indicated point?

• A. $1.96$
• B. $0$
• C. $0.5$
• D. $1$

Answer: (D)

Verified step by step guidance

1. Understand that the problem involves a standard normal distribution, which has a mean \(\mu = 0\) and a standard deviation \(\sigma = 1\).
2. Recognize that the shaded area to the left of the indicated point represents the cumulative probability \(P(Z \leq z)\) for some z-score \(z\).
3. Use the given cumulative probability value, which is 0.8413, and recall that this corresponds to the area under the standard normal curve to the left of the z-score.
4. Consult the standard normal distribution table (Z-table) or use a statistical software/calculator to find the z-score that corresponds to a cumulative probability of 0.8413.
5. Identify the z-score \(z\) such that \(P(Z \leq z) = 0.8413\). This z-score is the value you are asked to find.