The skewness of a binomial distribution is given by the formula (q-p)/sqrt(npq). Substituting p=0.4, q=0.6, and n=5, we get (0.6-0.4)/sqrt(5*0.4*0.6) = 0.2/sqrt(1.2) = 0.2/1.0954, which approximately equals 0.182. Given the provided answer key is 0.167, there may be a discrepancy in the calculation method or rounding used in the source.

A Bernoulli process is a sequence of independent random experiments, each having exactly two possible outcomes, often labeled as 'success' and 'failure'. The probability of success remains constant across all trials. This process serves as the foundation for the Binomial distribution, which models the number of successes in a fixed number of independent Bernoulli trials.

A core assumption of the Binomial distribution is that the probability of success, denoted as 'p', remains constant across all 'n' independent trials. If the probability of success changes from trial to trial, the process does not follow a Binomial distribution.

A binomial distribution is symmetrical when the probability of success (p) equals the probability of failure (q). Since p + q = 1, this condition is satisfied if and only if p = 0.5 (or 1/2). Both options (b) and (c) describe this same mathematical requirement, making them both correct conditions for symmetry.

The mean of a binomial distribution is defined as the product of the number of trials (n) and the probability of success (p). This is a fundamental property of the binomial distribution, representing the long-run average number of successes expected in n independent Bernoulli trials.

While the binomial distribution is mathematically defined for any positive integer n, it is most frequently utilized in statistical inference and large-scale modeling when n is large. Large n values facilitate the use of normal approximations, which are essential for conducting hypothesis tests and constructing confidence intervals efficiently in practical research scenarios.

A binomial distribution is negatively skewed (skewed to the left) when the probability of success (p) is greater than 0.5. In this scenario, the distribution has a longer tail on the left side because the probability mass is concentrated toward the higher end of the range of possible outcomes, making the mean less than the mode.

The binomial probability mass function is defined as P(X=x) = nCx * p^x * q^(n-x), where nCx is the binomial coefficient, p is the probability of success, and q is the probability of failure (1-p). The notation {nx} represents the combination of n items taken x at a time.

The hypergeometric distribution models the number of successes in a sequence of draws from a finite population without replacement. Because the items are not replaced, the composition of the population changes after each draw, causing the probability of success to vary across trials. This distinguishes it from the binomial distribution, where trials are independent and the probability remains constant.

The mean of a binomial distribution is np and the variance is npq. Since q = 1 - p and 0 < p < 1, it follows that 0 < q < 1. Therefore, np > npq, meaning the mean is always greater than the variance. The provided explanation in the source regarding the Central Limit Theorem is conceptually inaccurate for this specific property, but the answer choice is mathematically correct.