Question

If p = .1 and n = 5, then the corresponding binomial distribution is ________.

1) Right skewed
2) Left skewed
3) Symmetric
4) Bimodal

Answer 1

If p = 0.1 and n = 5, the corresponding binomial distribution is right skewed due to a low probability of success and a small number of trials.

Step-by-step explanation:

If p = 0.1 and n = 5, then the corresponding binomial distribution is right skewed. This is because the probability of success (p = 0.1) is much less than the probability of failure (q = 1 - p = 0.9), which means that successes are rare and the majority of the data will cluster at the lower end (few successes), with a long tail extending to the right towards the higher end (more successes). Since the number of trials n is 5, which is relatively small, and the probability of success p is only 0.1, the distribution will not be symmetrical. It cannot be left skewed because we would expect more occurrences of 0, 1, or 2 successes than 3, 4, or 5, given the low probability of success. The distribution is also not likely to be bimodal as the probability of getting an intermediate number of successes (such as 2 or 3) is still less than getting very few or none.