Question

let k be the number of successes (green) when the spinner is spun 4 times. the graph shows the distribution of k. slide the slider to change p. what effect does this have on the distribution? check all of the boxes that apply. the graph is always a binomial distribution no matter what p is, k can always be 0, 1, 2, 3, or 4. for values of p close to 0.5, the distribution is more symmetric. for values of p close to 1, youre most likely to get 3 or 4 successes in 4 spins. done

Explanation:

1. The spinner - spin scenario follows a binomial distribution as there are a fixed number of trials (4 spins), two possible outcomes (success - green or failure), and a constant probability of success $p$. So, the graph is always a binomial distribution.
2. Since the spinner is spun 4 times, the number of successes $k$ can be any non - negative integer from 0 to 4 regardless of the value of $p$.
3. In a binomial distribution $B(n,p)$ with $n$ trials, when $p = 0.5$, the distribution is symmetric. As $p$ gets closer to 0.5, the symmetry becomes more pronounced.
4. When $p$ is close to 1, the probability of success in each trial is high. So, in 4 spins, we are more likely to get a high number of successes (3 or 4).

Answer:

The graph is always a binomial distribution, No matter what $p$ is, $k$ can always be 0, 1, 2, 3, or 4, For values of $p$ close to 0.5, the distribution is more symmetric, For values of $p$ close to 1, you're most likely to get 3 or 4 successes in 4 spins.