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According to data released in $2016,69 \%$ of students in the United States enroll in college directly after high school graduation. Suppose a sample of 165 recent high school graduates is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability that at most $61 \%$ enrolled in college directly after high school graduation.

First, verify that the conditions of the Central Limit Theorem are met.
The Random and Independent condition holds assuming independence.
The Large Samples condition holds.
The Big Populations condition can reasonably be assumed to hold.

The probability is $\square$
(Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：First, verify that the conditions of the Central Limit Theorem are met. The Random and Independent condition holds assuming independence. The Large Samples condition holds. The Big Populations condition can reasonably be assumed to hold.

Step 2 ：Given values are: sample size \(n = 165\) and probability of success (enrollment in college) \(p = 0.69\).

Step 3 ：Calculate the mean and standard deviation. The mean is \(n \times p = 113.85\) and the standard deviation is \(\sqrt{n \times p \times (1 - p)} = 5.94\).

Step 4 ：Calculate the z-score for \(0.61n\). The z-score is \(\frac{0.61 \times n - \text{mean}}{\text{std_dev}} = -2.22\).

Step 5 ：Calculate the probability using the cumulative distribution function (CDF) of the normal distribution. The probability is approximately 0.013, or 1.3%.

Step 6 ：Final Answer: The probability is \(\boxed{0.013}\). This is a relatively low probability, indicating that it is unlikely to observe such a low enrollment rate in a random sample of 165 high school graduates, given that the overall enrollment rate is 69%.