Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of e so that the following is true. P(Zsc)=0.2420

Carry your Intermediate computations to at least four decimal places. Round your answer to two decimal places.

To solve the problem, we need to find the value of \( z \) such that the probability \( P(Z \leq z) = 0.2420 \), where \( Z \) follows the standard normal distribution.

### Step 1: Understand the Problem
The problem asks us to find the value of \( z \) such that the cumulative probability up to \( z \) under the standard normal distribution is 0.2420. In other words, we are looking for the \( z \)-score that corresponds to the 24.20th percentile of the standard normal distribution.

### Step 2: Use the Standard Normal Table or Calculator
To find the \( z \)-score, we can use a standard normal distribution table or a calculator that provides the inverse cumulative distribution function (often labeled as "invNorm" or similar).

### Step 3: Find the \( z \)-Score
Using the standard normal table or calculator:

- Look up the cumulative probability value of 0.2420 in the table, or use a calculator to find the corresponding \( z \)-score.
- The value that corresponds to \( P(Z \leq z) = 0.2420 \) is approximately \( z = -0.70 \).

### Step 4: Round the Answer
The \( z \)-score that corresponds to a cumulative probability of 0.2420 is approximately \(-0.70\) when rounded to two decimal places.

### Final Answer:
\[
z \approx -0.70
\]

Would you like any additional details or further assistance on this topic?

### 5 Related Questions:
1. How do you find the \( z \)-score for a different percentile, such as the 75th percentile?
2. What is the probability \( P(Z \leq 1.28) \) for a standard normal distribution?
3. How do you interpret the area under the standard normal curve?
4. What does it mean if a \( z \)-score is positive versus negative?
5. How can you use the \( z \)-score to determine the probability of values above or below a certain threshold?

**Tip:** Always ensure you're using the correct table or calculator setting when working with cumulative probabilities and the standard normal distribution.

Learn how to calculate the z-score for a cumulative probability of 0.2420 in the standard normal distribution. Follow a step-by-step solution using a standard normal table or calculator to find the corresponding z-score. Suitable for undergraduate level students and anyone studying statistics.

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