Final answer:
For a binomial distribution with 10 trials, the distribution is skewed left when the probability of success, p, is large (close to 1). This left skewness happens because there will be more high values and fewer low values.
Step-by-step explanation:
When considering a binomial distribution with 10 trials, the skewness of the distribution does depend on the value of the probability of success, p. For large values of p, meaning p is closer to 1, the distribution will be skewed to the left. This is because as p increases, the likelihood of success in each trial increases, and thus, the distribution tends to have more high values, and fewer low values, shifting the bulk of the distribution towards the upper end.
The skewness for a binomial distribution can be generally anticipated by considering the values of p. A high p value (close to 1) indicates a left-skewed distribution, while a low p value (close to 0) leads to a right-skewed distribution.
This asymmetry is evident because a high p means that there will be fewer failures and thus a pile-up of larger values on the right side of the mean, while a low p results in more failures and therefore a concentration of smaller values on the left side of the mean. The binomial distribution approaches symmetry when p is near 0.5, looking similar to a normal distribution.
It's important to remember that these skewness characteristics apply when other conditions are met, such as a sufficiently large number of trials. When p is very small or the number of trials is very large, the Poisson distribution may sometimes be used to approximate the binomial distribution.