Using a standard normal curve, find the proportion of data that falls below at or below a 𝑧𝑧-score of 1.22
(i.e. 𝑃𝑃(𝑍𝑍 ≤ 1.22))

To find the proportion of data that falls at or below a \( z \)-score of 1.22, we need to use the cumulative distribution function (CDF) for the standard normal distribution.

Using standard normal tables or a calculator:

\[
P(Z \leq 1.22) = 0.8888
\]

This means that approximately 88.88% of the data falls at or below a \( z \)-score of 1.22 on a standard normal distribution.

Would you like further details or clarification on how this value is determined?

Here are 5 related questions for further practice:

1. What is \( P(Z \leq -1.22) \)?
2. What is \( P(Z \geq 1.22) \)?
3. How do you calculate \( P(Z \leq 0) \) in a standard normal distribution?
4. What is the \( z \)-score corresponding to the 95th percentile?
5. How do you calculate the proportion between two \( z \)-scores, like \( P(0.5 \leq Z \leq 1.22) \)?

**Tip:** The area under the standard normal curve always equals 1, and it's symmetric around \( Z = 0 \). This makes it easy to calculate values for negative \( z \)-scores by reflecting across the mean.

Using a standard normal curve, find the proportion of data that falls below or at a z-score of 1.22 (i.e. P(Z ≤ 1.22))

Discover how to calculate the proportion of data below a z-score of 1.22 using the cumulative distribution function (CDF) of the standard normal distribution. Learn the steps to find P(Z ≤ 1.22), which equals 0.8888, indicating that approximately 88.88% of data lies below this z-score. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation