Suppose Z

follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c

so that the following is true.=

P

≤

0.66

≤

Z

c

0.2187

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

We are given the following probability:

\[
P(Z \leq c) = 0.2187
\]

Where \( Z \) is a standard normal variable, and we need to find the value of \( c \) such that the cumulative probability is 0.2187.

### Step 1: Understanding the problem
This means we need to find the z-score, \( c \), such that the area to the left of \( c \) under the standard normal curve is 0.2187. This can be done by finding the inverse of the cumulative distribution function (CDF) for a standard normal distribution.

### Step 2: Using the z-score table or calculator
To find \( c \), we look up the probability 0.2187 in a standard normal distribution table or use a calculator to find the corresponding z-score.

### Step 3: Calculating the z-score
Using the inverse CDF of the standard normal distribution, we get:

\[
c = \text{invNorm}(0.2187) \approx -0.78
\]

### Final Answer:
The value of \( c \) is approximately **-0.78**.

Would you like more details on how to use the table or the calculator?

---

Here are 5 related questions to deepen your understanding:
1. What is the standard normal distribution, and how is it used in probability?
2. How can you interpret a z-score in terms of standard deviations?
3. What is the difference between the cumulative distribution function (CDF) and the probability density function (PDF)?
4. How do you use a z-score table to find probabilities for standard normal distributions?
5. How does the symmetry of the normal distribution affect calculations involving z-scores?

**Tip:** When using z-tables, always check whether the table shows cumulative probabilities from the left or the right, as this can change your lookup approach.

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true: P(Z ≤ c) = 0.2187. Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Learn how to find the z-score corresponding to a cumulative probability of 0.2187 in a standard normal distribution. This problem covers key concepts in statistics, including the use of the inverse CDF function and properties of the normal distribution. Ideal for undergraduate or AP Statistics students.

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