Question
Find the \( z \) value to the right of the mean so that \( 61.79 \% \) of the area under the distribution curve lies to the left of it. Use The standard Normal Distribution Table and enter the answer to 2 decimal places. \[ z= \]
Ask by Ellis Lang. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z = 0.30 \)
Solution
1. We are given that \( P(Z < z) = 0.6179 \).
2. Consult the standard Normal Distribution table to find the \( z \) value for which the cumulative area is approximately 0.6179. Looking at the table, we see that when \( z = 0.30 \), the cumulative probability is 0.6179.
3. Therefore, the \( z \) value is:
\[
z = 0.30.
\]
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Simplify this solution Beyond the Answer
To find the \( z \) value such that \( 61.79 \% \) of the area lies to the left of it, we need to first convert that percentage into a decimal, which is \( 0.6179 \). Next, we look for the corresponding \( z \) value in the standard Normal Distribution Table. The value that gives an area of approximately \( 0.6179 \) to the left is about \( z = 0.31 \) (you may find slightly different values depending on the table, but they should be close). Thus, we can conclude: \[ z = 0.31 \]
