8
AssignmentMultiple Select

Expected Value

Question 8 • CREDIT RE-SEAT MNPS Integrated Math III IC S2 26-27

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.

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

Explanation

Each spin has the same probability p of success, and there are 4 spins, so k follows a binomial distribution. The number of successes ranges from 0 to 4; when p is exactly 0 or 1, the distribution concentrates on one of those outcomes. At p = 0.5, outcomes on either side of 2 successes have matching probabilities, making the distribution symmetric. When p is close to 1, getting 3 or 4 successes is most likely.

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