Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 28. 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 28. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is a result of 1 peas with green pods a result that is significantly low? Why or why not?

a. Let X be the number of peas with green pods in a group of 28. The probability of a pea having green pods, p = 0.25.
a.1. Mean:
E(X) = np = 28 \times 0.25 = 7
a.2. Standard Deviation:
SD(X) = \sqrt{np(1-p)} = \sqrt{28 \times 0.25 \times 0.75} = \sqrt{5.25} \approx 2.29

b. Range Rule of Thumb: According to the range rule of thumb, results that are significantly low are those that fall below E(X) - 2 \times SD(X) , and results that are significantly high are those that fall above E(X) + 2 \times SD(X) .
Significantly\;Low = 7 - 2 \times 2.29 \approx 2.42
Significantly\;High=7+2\times2.29\approx11.58

c. Result of 1 pea with green pods:
Since 1 pea with green pods is below the significantly low range of 2.42, it is considered a significantly low result. The probability of getting only 1 green pod in a group of 28 is fairly low based on the distribution, so it would be considered significant.

\textbf{Answer:} The result of 1 pea with green pods is significantly low.