Question

a survey of 200 randomly selected high school students determined that 150 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 0.750. (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 exactly of them play organized sports. b. if 1,000 high school students were sampled, it would be expected that about of them play organized sports.

Explanation:

Step1: Calculate probability for part (a)

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes (students who play organized sports) is $n = 150$ and the total number of outcomes (total students surveyed) is $N=200$. So $P=\frac{150}{200}=0.750$.

Step2: Interpret probability for part (b)

The probability of $0.750$ means that on average, for a large - sample of students. If we sample $n = 1000$ students, we expect the number of students who play organized sports to be $1000\times0.750 = 750$. Probability gives an expected value, not an exact value for a sample. So we use "about" instead of "exactly".

Answer:

(a) $0.750$
(b) B. If 1,000 high school students were sampled, it would be expected that about 750 of them play organized sports.