1. **State the problem:** We have groups of 30 peas, each pea has a 0.75 probability of having green pods. We want to find the mean and standard deviation of the number of peas with green pods in each group. 2. **Identify the distribution:** The number of peas with green pods follows a binomial distribution with parameters $n=30$ and $p=0.75$. 3. **Formulas:** - Mean (expected value) of a binomial distribution: $$\mu = np$$ - Standard deviation of a binomial distribution: $$\sigma = \sqrt{np(1-p)}$$ 4. **Calculate the mean:** $$\mu = 30 \times 0.75 = 22.5$$ 5. **Calculate the standard deviation:** $$\sigma = \sqrt{30 \times 0.75 \times (1 - 0.75)} = \sqrt{30 \times 0.75 \times 0.25} = \sqrt{5.625} \approx 2.3717$$ **Final answers:** - Mean number of peas with green pods: $22.5$ - Standard deviation: approximately $2.37$