Question

Which of the following is true with respect to the binomial distribution?

As the sample size increases, the expected value of the random variable decreases.

The binomial distribution becomes more skewed as the sample size is increased for a given probability of success.

The binomial distribution tends to be more symmetric as p approaches 0.5.

In order for the binomial distribution to be skewed, the sample size must be quite large. 2 points

Answer 1

option A is incorrect because the expected value never decreases when we increase the sample size

option B is incorrect because we know that the binomial distribution becomes more symmetrical when the sample size increases.

option C is correct because we know that as the p value tends to 0.5, the binomial distribution becomes more symmetric and follows normal distribution more accurately

option D is incorrect because larger sample size means more symmetric data distribution, so it is not skewed.

option C is correct answer