A survey of 900 randomly selected high school students determined that 164 play organized sports. (a) What is the probability that a randomly selected high school student plays organized sports? (b) Interpret this probability. (a) The probability that a randomly selected high school student plays organized sports is 0.182 . (Round to the nearest thousandth as needed.) (b) Choose the correct answer below. (Type a whole number.) A. If 1,000 high school students were sampled, it would be expected that about $\square$ of them play organized sports. B. If 1,000 high school students were sampled, it would be expected that exactly of them play organized sports.

Step 1 ：Given that a survey of 900 randomly selected high school students determined that 164 play organized sports.

Step 2 ：To find the probability that a randomly selected high school student plays organized sports, we divide the number of students who play organized sports by the total number of students surveyed. The formula for probability is \(P(A) = \frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes in the sample space.

Step 3 ：Substituting the given values into the formula, we get \(P(A) = \frac{164}{900} = 0.18222222222222223\).

Step 4 ：So, the probability that a randomly selected high school student plays organized sports is approximately 0.182 or 18.2%.

Step 5 ：Now, to answer the second part of the question, we need to apply this probability to a sample of 1000 students. The expected number of students playing sports in a sample of 1000 can be found by multiplying the total number of students in the sample by the probability of a student playing sports.

Step 6 ：Substituting the given values into the formula, we get \(1000 * 0.18222222222222223 = 182.22222222222223\).

Step 7 ：Rounding to the nearest whole number, we get 182.

Step 8 ：Final Answer: If 1,000 high school students were sampled, it would be expected that about \(\boxed{182}\) of them play organized sports.