Question

You roll a six-sided die 12 times and are interested in how many

1."1"s you are likely to get (= how many times it lands with the side showing one dot, facing up)

2."numbers less than 5" you are likely to get (= how many times it lands on any of the sides that show 1, 2, 3, or 4 dots, facing up).

3."numbers more than 4" you are likely to get (= how many times it lands on either of the sides that show 5 or 6 dots, facing up).

Sketch the resultant binomial distributions.

How will you find the mode for the above binomial distributions?

Answer 1

To find the mode for the binomial distributions, calculate the probabilities for each outcome and identify the one with the highest probability. Sketch the resultant binomial distributions to visualize the probabilities.

Step-by-step explanation:

To find the mode for the binomial distributions, we need to determine the outcome with the highest frequency. In this case, we have three different outcomes: 1, numbers less than 5, and numbers more than 4. We will calculate the probabilities for each outcome and identify the one with the highest probability.

1. To find the mode for the number of 1s, we will use the binomial distribution formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (12), k is the number of 1s (0 to 12), and p is the probability of getting a 1 on each trial (1/6).

2. To find the mode for the number of numbers less than 5, we will sum the probabilities for getting 1, 2, 3, or 4. This can be calculated by adding the probabilities of each individual outcome from step 1.

3. To find the mode for the number of numbers more than 4, we will subtract the probability of getting numbers less than 5 from 1, as the remaining probability will be for numbers more than 4.

Sketching the resultant binomial distributions will visually display the probabilities for each outcome.