Question

consider the given probability histogram of a binomial
random variable.
what are the center and shape of the distribution?
binomial random variable
center: 5.4
(n = 6, p = 0.9)
shape: skewed right
center: 5.4
shape: skewed left
center: 6
shape: skewed left
center: 6
shape: approximately normal

Explanation:

Step1: Calculate the center (mean) of the binomial distribution

The mean of a binomial distribution is given by the formula \(\mu = np\). Here, \(n = 6\) and \(p=0.9\). So, \(\mu=6\times0.9 = 5.4\).

Step2: Analyze the shape of the binomial distribution

For a binomial distribution \(B(n,p)\), if \(p>0.5\), the distribution is skewed left. Here \(p = 0.9>0.5\) and \(n = 6\).

Answer:

Center: \(5.4\)
Shape: skewed left