Question

a survey of 400 randomly selected high school students determined that 284 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 0.71
(round to the nearest thousandth as needed.)
(b) choose the correct answer below.
(type a whole number)
oa. if 1,000 high school students were sampled, it would be expected that exactly of them play organized
sports.
ob. if 1,000 high school students were sampled, it would be expected that about of them play organized
sports

Explanation:

Step1: Calculate the probability for part (a)

The formula for probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (students who play organized sports) is \(n = 284\), and the total number of outcomes (total students surveyed) is \(N=400\). So, \(P=\frac{284}{400}=0.71\)

Step2: Interpret the probability for part (b)

Probability gives an estimate, not an exact value. If the probability that a single - student plays organized sports is \(p = 0.71\), and we have a sample of \(N'=1000\) students. The expected number of students who play organized sports is \(E=n'=N'\times p\). Substitute \(N' = 1000\) and \(p=0.71\) into the formula: \(n'=1000\times0.71 = 710\)

Answer:

(a) \(0.71\)
(b) B. If 1,000 high school students were sampled, it would be expected that about \(710\) of them play organized sports