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Pick one of the points on your graph from Part 2 that is not the one corresponding to y = 0.5. Write a probability statement involving the x- and y- coordinate values that describes how they relate to each other.

Let's choose the point \( (581.96, 0.66) \) from the graph.

The probability statement for this point would be:

\[
P(X \leq 581.96) = 0.66
\]

This means that there is a 66% probability that a random variable \( X \) (following this normal distribution) will take on a value less than or equal to 581.96. In terms of cumulative probability, 581.96 is the 66th percentile of this distribution.

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

Here are five related questions that could extend your understanding:

1. How do we interpret a cumulative probability of 0.22 in terms of percentile?
2. How would you calculate the probability that \( X \) is greater than 581.96?
3. What does the symmetry of the normal distribution imply about points above and below the mean?
4. How can you find the mean and standard deviation from a cumulative distribution function?
5. Why is the cumulative probability 0.5 at the mean value (570 in this case)?

**Tip:** Cumulative Distribution Functions (CDFs) are useful because they give the probability that a variable is less than or equal to a particular value, which can help find percentiles and assess likelihoods directly.

Explore how to interpret cumulative probability for a normal distribution with CDF. Learn to make probability statements for points on the CDF graph, like P(X ≤ 581.96) = 0.66, representing a 66% probability. Ideal for students in Grades 11-12.

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