Final answer:
It is true that a binomial distribution with n=10 and p=0.5 would take on normal distribution properties and appear normally distributed as the conditions for normal approximation are met.
Step-by-step explanation:
It is true that a binomial distribution with n=10 and p=0.5 would approximate normal distribution properties and appear normally distributed. The binomial distribution has certain characteristics, like a fixed number of independent trials and two outcomes (success or failure) with each trial having the same probability of success, p. If X is the binomial random variable, then X ~ B(n, p). The normal approximation of a binomial distribution is often used when the mean μ = np and standard deviation σ = √npq satisfy the conditions np > 5 and nq > 5, which they do in this case (n=10, p=0.5, q=0.5).
Furthermore, for calculations, we may add or subtract 0.5 to the number of successes (x) to get a better approximation. Since np and nq are both equal to 5 in this scenario, the approximation to the normal distribution is acceptable but not perfect. It's also notable that when p = 0.5, the binomial distribution is symmetric, which makes it more closely resemble a normal distribution. However, the approximation improves with larger n values.