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According to the High School Athletics Participation Survey, 55% of students enrolled in high school participate...

According to the High School Athletics Participation Survey, 55% of students enrolled in high school participate in athletic programs. Suppose 12 high school students are randomly selected and the number who participate in athletic programs is recorded. Round probabilities to 4 decimal places.

  1. Explain why this is a binomial experiment.
  2. Find and interpret the probability that exactly 7 high school students participate in athletic programs.
  3. Find and interpret the probability that fewer than 7 high school students participate in athletic programs.
  4. Find and interpret the probability that at least 7 high school students participate in athletic programs.
  5. Compute the mean and standard deviation of the binomial random variable
Math   Statistics-And-Probability   
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Answer #1

A) This is a binomial experiment as there are only two possible outcomes - participation in athletic programs and non-participation in athletic programs

B) p= 0.55, Number of trials = n = 12

The binomial formula is:

We need to find: P(X = 12) = 12C7 * (0.55)7(0.45)5 = 0.222

C) P(X < 7) = Σ P(X = i), i from 1 to 6

P(X < 7) = P(X = 0) + P(X=1) + .. P(X=6) = 0.473

D) P(X>=7) = 1 - P(X < 7) = 1 - 0.473 = 0.527

E) Mean = np = 0.55*12 = 6.6

Standard deviation = √npq = √(12*0.55*0.45) = 1.723

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