Question

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 22. Use the range rule of thumb to find the value separating results that are significantly low

Answer 1

Definition

According the range rule of thumb, most values should lie within 2 standard deviations of the mean.

Given:

The probability that a pea has a green pod = 0.75

Number of groups = 22

The formula to find the value seperating the results that are significantly low is:

$=\text{ mean - 2 }\times\text{ standard deviation}$

The mean and standard deviation can be found using the formula:

$\begin{gathered} \text{mean = np} \\ \text{standard deviation = }\sqrt[]{npq} \end{gathered}$

Where n is the numble of samples

p is the probability of success

q is the probability of failure

Substituting we have:

$\begin{gathered} \operatorname{mean}\text{ = 22 }\times\text{ 0.75} \\ =\text{ 16.5} \\ \text{Standard deviation = }\sqrt[]{22\times0.75\times(1-0.75)} \\ =\text{ 2.031} \end{gathered}$

Using the range rule, the value seperating results that are significantly low is:

$\begin{gathered} =\text{ 16.5 - 2}\times2.031 \\ =\text{ 12.438} \end{gathered}$

Answer: 12.438