Suppose that 3% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 35 students who have recently taken the test. (Round your probabilities to three decimal places.)

(a) What is the probability that exactly 1 received a special accommodation?

Let's solve this problem using the binomial probability formula, which is suitable since we are dealing with a fixed number of independent trials (students) and two possible outcomes: receiving a special accommodation or not.

### Binomial Probability Formula:
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]

Where:
- \( n = 35 \) is the number of trials (students).
- \( k = 1 \) is the number of students who received special accommodation.
- \( p = 0.03 \) is the probability of receiving special accommodation.
- \( \binom{n}{k} \) is the binomial coefficient.

Substituting the given values:

\[
P(X = 1) = \binom{35}{1} (0.03)^1 (1 - 0.03)^{35 - 1}
\]

Let's compute this probability step-by-step.The probability that exactly 1 student out of 35 received a special accommodation is approximately \( 0.373 \).

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

### Related Questions:
1. What is the probability that no students received special accommodation?
2. What is the probability that at least 2 students received special accommodations?
3. What is the expected number of students receiving special accommodations?
4. How would the probability change if the sample size were increased to 50 students?
5. What is the variance and standard deviation of students receiving special accommodations?

**Tip:** Binomial distributions are useful for modeling scenarios with fixed trials, two outcomes, and constant probabilities.

Suppose that 3% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 35 students who have recently taken the test. (a) What is the probability that exactly 1 received a special accommodation?

Calculate the probability that exactly 1 out of 35 students received special accommodations during the SAT using the binomial distribution formula. This solution covers probability concepts, binomial formulas, and step-by-step calculations for high school students.

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