Question

Take a spin An online spinner has two colored regions-blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is $0.80$. Assume for now that this claim is correct. Suppose we spin the spinner$12$ times and let $X=$ the number of times it lands in the blue region. Make a graph of the probability distribution of X. Describe its shape.

Short answer

The left tail of the graph is much longer than the right tail, indicating that the distribution is skewed to the left.

Step-by-step solution

Given information

Given:

The Probability of success $\left(p\right)=0.80$

The Number of trials $\left(n\right)=12$

Simplification

Assume X to be the random variable that reflects the number of times the spinner falls in the blue region, with parameters $n=12$and $p=0.80$.

The probability distribution can be expressed as follows:

$P(X=r){=}^{12}{C}_r\times (0.80{)}^r\times (1-0.80{)}^{12-r}$

Graph: The probability distribution of X can be represented as follows:

The left tail of the graph is much longer than the right tail, indicating that the distribution is skewed to the left.