https://file.aiquickdraw.com/mathbot/file/1727109132801mckbebzz.jpg

The problem is asking to calculate the z-score for a grade equal to 9.8 using the provided data and a given standard deviation (s.d.) of 1.86. Here's how you can solve this:

### Z-score Formula:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X\) is the value for which you want to calculate the z-score (in this case, \(X = 9.8\)),
- \(\mu\) is the mean (average) of the grades,
- \(\sigma\) is the standard deviation (in this case, \(\sigma = 1.86\)).

### Step 1: Calculate the Mean (\(\mu\)) of the Grades
We need to find the mean grade from the table. The grades are:
\[
4.4, 8.9, 1.2, 8.1, 7.4, 8.7, 5.3, 7.2, 6.8, 9.2
\]

Now, let's calculate the mean (\(\mu\)). I will calculate it now.The mean of the grades (\(\mu\)) is approximately 6.72.

### Step 2: Calculate the Z-score
Using the z-score formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where:
- \(X = 9.8\) (the grade for which we are calculating the z-score),
- \(\mu = 6.72\) (the mean of the grades),
- \(\sigma = 1.86\) (the given standard deviation).

Now, let's calculate the z-score.The z-score for a grade of 9.8 is approximately **1.6559**.

Would you like further details on this calculation, or have any questions?

Here are five related questions for further exploration:
1. How do z-scores help in comparing values from different distributions?
2. What is the interpretation of a positive z-score?
3. How would you calculate the z-score if the grade was below the mean?
4. Can you calculate the probability of obtaining a grade higher than 9.8 based on the z-score?
5. How would you verify whether the data follows a normal distribution?

**Tip:** A z-score of 1.6559 means that the grade of 9.8 is about 1.66 standard deviations above the mean.

Calculate the z-score for a grade equal to 9.8 with a standard deviation of 1.86 using the provided data for time spent and grades.

Learn how to calculate the z-score for a grade of 9.8 using the formula z = (X - μ) / σ. The mean grade is calculated from the dataset, and a standard deviation of 1.86 is provided. This example is suitable for students in undergraduate-level statistics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation