Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 10 . Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of peas with green pods in the groups of 10. The value of the mean is \( \mu= \) \( \square \) peas. (Type an integer or a decimal. Do not round.) The value of the standard deviation is \( \sigma= \) \( \square \) peas. (Round to one decimal place as needed.) b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. Values of \( \square \) peas or fewer are significantly low. (Round to one decimal place as needed.) Values of \( \square \) peas or greater are significantly high. (Round to one decimal place as needed.) c. Is a result of 9 peas with green pods a result that is significantly high? Why or why not? The result \( \square \) significantly high because 9 peas with green pods is \( \square \) \( \square \) peas. (Round to one decimal place as needed.)

To find the mean and standard deviation for the number of peas with green pods in groups of 10, we will use the properties of a binomial distribution. Here, the probability of a pea having green pods (success) is \( p = 0.75 \), and the number of trials (peas) is \( n = 10 \). a. The mean \( \mu \) can be calculated as: \[ \mu = n \cdot p = 10 \cdot 0.75 = 7.5 \] The standard deviation \( \sigma \) is given by the formula: \[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} = \sqrt{10 \cdot 0.75 \cdot 0.25} \approx \sqrt{1.875} \approx 1.4 \] So, the values are: Mean \( \mu = \) \( 7.5 \) peas. Standard deviation \( \sigma = \) \( 1.4 \) peas. b. Using the range rule of thumb, we find that results outside \( \mu \pm 2\sigma \) are significantly low or high. Let's calculate it: - Significantly low = \( \mu - 2\sigma = 7.5 - 2 \times 1.4 = 4.7 \) - Significantly high = \( \mu + 2\sigma = 7.5 + 2 \times 1.4 = 10.3 \) Values of \( \) 4.7 peas or fewer are significantly low. Values of \( \) 10.3 peas or greater are significantly high. c. To determine if a result of 9 peas with green pods is significantly high, we can compare it to the identified threshold for significantly high results: Since 9 is less than 10.3, the result \( 9 \) is \( \text{not} \) significantly high because 9 peas with green pods is \( \text{below} \) \( 10.3 \) peas.