In this case, we can model the number of peas with green pods as a binomial distribution. The binomial distribution has two parameters: the number of trials $n$ and the probability of success on each trial $p$.

• $n = 32$ (since there are 32 offspring peas in the group),
• $p = 0.75$ (the probability that a pea has green pods).

a) To find the mean ($\mu$) of a binomial distribution, use the formula:

$\mu = n \cdot p$ Substitute the values: $\mu = 32 \cdot 0.75 = 24$ So, the mean is $\mu = 24$ peas.

Do you need details about how to find the standard deviation, or any other clarification?

Here are some related questions to further explore:

1. How do you calculate the standard deviation for a binomial distribution?
2. What would be the variance for this binomial distribution?
3. How would the mean change if $n$ were increased to 50?
4. What is the probability of getting exactly 24 peas with green pods in a group of 32?
5. How does the binomial distribution differ from the normal distribution?

Tip: For a binomial distribution, the standard deviation helps measure the spread of the outcomes around the mean, and it is closely tied to both the number of trials and the success probability.