What is the Z-value that corresponds to an confidence interval?

Ask by Peterson Peterson. in the United States

Jan 24,2025

Question

What is the Z-value that corresponds to an $$ 78 \% $$ confidence interval? $$ \begin{array}{llll}	ext { A) }-2.1 & 	ext { B) } 1.23 & 	ext { C) } 1.20 & 	ext { D) }-1.61\end{array} $$

UpStudy AI · Accepted Answer

To determine the Z-value corresponding to a **78% confidence interval**, follow these steps:

1. **Understand the Confidence Interval:**
   - A 78% confidence interval means that 78% of the data lies within this range in a standard normal distribution.
   - This leaves $$ \frac{100\% - 78\%}{2} = 11\% $$ in each tail of the distribution.

2. **Find the Corresponding Z-Value:**
   - We need the Z-value where the cumulative probability up to that point is $$ 78\% + 11\% = 89\% $$.
   - Using standard normal distribution tables or a calculator, the Z-value that corresponds to a cumulative probability of approximately 0.89 is **1.23**.

3. **Select the Correct Option:**
   - Among the given choices, **1.23** is the correct Z-value.

**Answer:** B) 1.23
The Z-value for a 78% confidence interval is 1.23.

What is the Z-value that corresponds to an confidence interval?

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