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The problem asks to find the probability that a given score is less than 1.05 using a normal distribution. Here's a breakdown of the situation based on the image:

1. The scores are normally distributed with a mean of 0 and a standard deviation of 1.
2. The task is to determine which graph correctly represents the cumulative area under the curve to the left of \( x = 1.05 \), which corresponds to finding \( P(X < 1.05) \).

### Standard Normal Distribution

For a standard normal distribution (mean = 0, standard deviation = 1), we need to find the cumulative probability for \( z = 1.05 \).

Using the Z-score table, \( P(Z < 1.05) \approx 0.8531 \).

This means that about 85.31% of the data lies below a Z-score of 1.05, so the correct graph should show an area under the curve to the left of \( x = 1.05 \) that covers about 85% of the total area.

### Graph Interpretation

Based on the question:
- The correct graph should shade a large portion of the left side of the curve (about 85%).
- The peak should be centered at \( x = 0 \), with a standard bell curve extending on both sides.

Graph **C** appears to match this description since it shows most of the area under the curve shaded to the left of \( x = 1.05 \), which is consistent with the solution from the Z-score table.

### Answer: 
The correct option is **C**.

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Would you like further details on how this problem is solved or explanations of related concepts?

Here are five related questions you might find useful:
1. How do you use a Z-score table to find probabilities?
2. What is the standard normal distribution, and why is it important?
3. How do you calculate the Z-score for a data point from any normal distribution?
4. How do cumulative probabilities work in a normal distribution?
5. What is the significance of the area under the curve in probability?

**Tip:** When working with normal distributions, the Z-score allows you to compare values from any normal distribution to the standard normal distribution.

Assume that a randomly selected subject is given a score density test. These test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.05 and draw a sketch of the region. Select the region. Choose the correct graph below.

Learn how to calculate the probability that a score is less than 1.05 using the standard normal distribution. This problem involves key statistical concepts such as Z-scores, cumulative probability, and graphical interpretation of normal curves. Suitable for students in Grades 10-12.

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