Use the range rule of thumb to identify significantly low or high values in the results:
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 14 . 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 14 .
The value of the mean is $\mu=10.5$ peas.
(Type an integer or a decimal. Do not round.)
The value of the standard deviation is $\sigma=1.6$ 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 peas or fewer are significantly low.
(Round to one decimal place as needed.)

Step 1 ：Given that the probability of a pea having green pods is 0.75, and the peas are randomly selected in groups of 14.

Step 2 ：The mean (\(\mu\)) of the number of peas with green pods in a group of 14 is calculated as \(\mu = 0.75 \times 14 = 10.5\) peas.

Step 3 ：The standard deviation (\(\sigma\)) is calculated as \(\sigma = \sqrt{14 \times 0.75 \times (1-0.75)} = 1.6\) peas (rounded to one decimal place).

Step 4 ：The range rule of thumb states that the range of a set of data is approximately four times the standard deviation. Therefore, the range of the number of peas with green pods in a group of 14 is \(4 \times \sigma = 4 \times 1.6 = 6.4\).

Step 5 ：Values that are significantly low or high are those that are more than two standard deviations away from the mean. Therefore, the significantly low value is \(\mu - 2\sigma = 10.5 - 2 \times 1.6 = 4.1\) and the significantly high value is \(\mu + 2\sigma = 10.5 + 2 \times 1.6 = 16.9\).

Step 6 ：Final Answer: Values of peas that are less than \(\boxed{4.1}\) are significantly low. Values of peas that are greater than \(\boxed{16.9}\) are significantly high.