AP Statistics 6.10 Setting Up a Test for the Difference of Two Population Proportions- MCQs - Exam Style Questions

This is a binomial probability problem.To escape experimentation, you must get 8 or more questions correct (i.e., 8, 9, or 10 correct) .

The parameters for the binomial distribution are:
–   Number of trials, $n = 10$ (ten questions).
–   Probability of success, $p = 0.5$ (guessing on a true-false test).

We need to find $P(X \ge 8) = P(X=8) + P(X=9) + P(X=10)$.
The binomial formula is $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$.

1.   $P(X=8) = \binom{10}{8} (0.5)^8 (0.5)^2 = 45 \times (0.5)^{10} \approx 0.0439$
2.   $P(X=9) = \binom{10}{9} (0.5)^9 (0.5)^1 = 10 \times (0.5)^{10} \approx 0.0098$
3.   $P(X=10) = \binom{10}{10} (0.5)^{10} (0.5)^0 = 1 \times (0.5)^{10} \approx 0.0010$

Adding these probabilities together: $0.0439 + 0.0098 + 0.0010 = 0.0547$.

✅ Answer: (D)