Question

consider the given probability histogram of a binomial random variable. what are the center and shape of the distribution? binomial random variable $(n = 5, p = 0.5)$ center: 2 shape: symmetric center: 2.5 shape: symmetric center: 2.5 shape: slightly skewed center: 3 shape: uniform

Explanation:

Step1: Calculate the center (mean) of binomial distribution

The formula for the mean of a binomial distribution is $\mu = np$. Given $n = 5$ and $p=0.5$, we have $\mu=5\times0.5 = 2.5$.

Step2: Analyze the shape

For a binomial distribution $B(n,p)$, when $p = 0.5$, the distribution is symmetric. Here $n = 5$ and $p = 0.5$, so the shape is symmetric.

Answer:

Center: 2.5, Shape: symmetric