91Ó°ÊÓ

It is given that a group of 10 peas is examined. The probability of a pea with green pods is equal to 0.75.

a.

Here, the probability of a pea with a green pod is given asp=0.75.

The probability of a pea with any other colored pod is computed below:

$$\begin{gathered} q=1-p \\ =1-0.75 \\ =0.25 \end{gathered}$$

The number of trials (n) is equal to 10.

Thus, the mean value is given as follows:

$$\begin{gathered} \mathrm{μ}=np \\ =\left(10\right)\left(0.75\right) \\ =7.5 \end{gathered}$$

Therefore, the mean number of peas with green pods is equal to 7.5.

The standard deviation is computed below:

$$\begin{gathered} \mathrm{σ}=\sqrt{npq} \\ =\sqrt{\left(10\right)\left(0.75\right)\left(0.25\right)} \\ =1.369 \\ ≈1.4 \end{gathered}$$

Therefore, the standard deviation of the number of peas with green pods is equal to 1.4.

b.

By using the range rule of thumb, the significantly low number of peas with green pods are computed below:

$$\begin{gathered} \mathrm{μ}-2\mathrm{σ}=7.5-\left(2\right)\left(1.4\right) \\ =4.7 \end{gathered}$$

Thus, the significantly low number of peas with green pods is4.7or less.

The significantly high number of peas with green pods are computed below:

$$\begin{gathered} \mathrm{μ}+2\mathrm{σ}=7.5+\left(2\right)\left(1.4\right) \\ =10.3 \end{gathered}$$

Thus, the significantly high number of peas with green pods is10.3 or more.

Moreover, the values that are not significant will lie between 4.7 and 10.3.

c.

Here, the value of 9 lies between 4.7 and 10.3.

Therefore, the value of 9 peas with green pods cannot be considered significantly high as it is less than 10.3.