Question

Which of the following are true statements? I. The histogram of a binomial distribution with p = .5 is always symmetric. II. The histogram of a binomial distribution with p = .9 is skewed to the right. III. The histogram of a geometric distribution with is always decreasing. Group of answer choices None of the above gives the complete set of complete responses. I and III I and II I, II, and III II and III

Answer 1

The correct statements about histograms of binomial and geometric distributions are that a binomial distribution with p = 0.5 is always symmetric, and a geometric distribution's histogram is always decreasing.

Step-by-step explanation:

The student asks which statements are true regarding histograms of binomial distributions and geometric distributions. Regarding the binomial distribution:

• I. For p = 0.5, the binomial distribution is always symmetric, which is true because the probability of success and failure are the same.
• II. For p = 0.9, the binomial distribution is skewed to the right. This is false; with a high probability of success, the distribution is skewed to the left.

For the geometric distribution:

• III. The statement that the histogram of a geometric distribution is always decreasing is true. The probability of the first success decreases as the number of trials increases.

Based on the analysis, the correct answer is I and III.