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.

Explanation:

1. The situation of spinning a spinner a fixed number of times with two - possible outcomes (success - green or failure - non - green) follows a binomial distribution, so the graph is always a binomial distribution.
2. Since the spinner is spun 4 times, the number of successes \(k\) can take values from 0 (no green) to 4 (all green).
3. In a binomial distribution \(B(n,p)\), 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 spin is high. So, in 4 spins, getting 3 or 4 successes is more likely.

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.