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 © 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 peas.
(Type an integer or a decimal. Do not round.)
The value of the standard deviation is 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.)
Values of 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 significantly high because 9 peas with green pods is
peas.
(Round to one decimal place as needed.)

Ask by Hills Howell. in the United States

Mar 20,2025

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 10 . Complete parts (a) through © 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 peas.
(Type an integer or a decimal. Do not round.)
The value of the standard deviation is 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.)
Values of 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 significantly high because 9 peas with green pods is
peas.
(Round to one decimal place as needed.)

Ask by Hills Howell. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

**(a)**  
The number of peas with green pods follows a binomial distribution with $$ n = 10 $$ and $$ p = 0.75 $$. The mean is given by  
$$
\mu = np = 10 \times 0.75 = 7.5 \text{ peas}.
$$  
The standard deviation is  
$$
\sigma = \sqrt{np(1-p)} = \sqrt{10 \times 0.75 \times 0.25} = \sqrt{1.875} \approx 1.4 \text{ peas}.
$$

**(b)**  
Using the range rule of thumb, results are considered significantly low if they are less than  
$$
\mu - 2\sigma = 7.5 - 2(1.4) = 7.5 - 2.8 = 4.7 \text{ peas}.
$$  
Similarly, results are significantly high if they exceed  
$$
\mu + 2\sigma = 7.5 + 2(1.4) = 7.5 + 2.8 = 10.3 \text{ peas}.
$$

Thus, values of $$4.7$$ peas or fewer are significantly low, and values of $$10.3$$ peas or greater are significantly high.

**(c)**  
A result of 9 peas with green pods is not significantly high because 9 is less than the high threshold of $$10.3$$ peas. In other words,  
$$
9 < \mu + 2\sigma = 10.3 \text{ peas},
$$  
so 9 peas does not meet the criterion for being significantly high.
**(a)** Mean ($$ \mu $$) = 7.5 peas Standard Deviation ($$ \sigma $$) ≈ 1.4 peas **(b)** Significantly low: 4.7 peas or fewer Significantly high: 10.3 peas or greater **(c)** A result of 9 peas with green pods is not significantly high because 9 is less than 10.3 peas.

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