Question

match \\(n = 4\\), \\(n = 8\\), \\(n = 12\\) with the correct graph. each histogram shown below represents part of a binomial distribution. each distribution has the same probability of success \\(p\\) but different numbers of trials \\(n\\).

histogram (a) has the number of trials \\(n = 12\\).
histogram (b) has the number of trials \\(n = 4\\).
histogram (c) has the number of trials \\(n = 8\\).

what happens as the value of \\(n\\) increases and the probability of success remains the same?

a. as \\(n\\) increases, the distribution becomes more skewed right.
b. as \\(n\\) increases, the distribution becomes more symmetric.
c. as \\(n\\) increases, the distribution becomes more skewed left.

Explanation:

Analyze the effect of increasing n on binomial distribution shape

As the number of trials \(n\) in a binomial distribution increases while the probability of success \(p\) remains constant, the distribution becomes more symmetric and approaches a normal distribution shape (by the Central Limit Theorem).

Evaluate the given options

• Option A states that the distribution becomes more skewed right, which is incorrect.
• Option B states that the distribution becomes more symmetric, which is correct.
• Option C states that the distribution becomes more skewed left, which is incorrect.

Answer:

• A. As n increases, the distribution becomes more skewed right.
• B. As n increases, the distribution becomes more symmetric. (Correct answer)
• C. As n increases, the distribution becomes more skewed left.