Chapter PV, Problem 2RE

(a)

To determine

To explain is the sampling distribution model for the sample proportion likely to be normal.

Answer to Problem 2RE

Yes, the sampling distribution model for the sample proportion is likely to be normal.

Explanation of Solution

It is given in the question that medical literature says that about $8\%$ of males are colorblind. A university’s introductory psychology course is taught in a large lecture hall. Among the students there are $325$ males. Thus, the sampling distribution model for the sample proportion is likely to be normal because it satisfy the condition of the normal, that is, the sample will have at least $10$ successes and $10$ failures, as,

  $\begin{array}{l}np=26>10\\ n(1-p)=299>10\end{array}$

(b)

To determine

To find out what is the mean and standard deviation of this sampling distribution model.

Answer to Problem 2RE

Mean is $26$ and standard deviation is $4.9$ .

Explanation of Solution

It is given in the question that medical literature says that about $8\%$ of males are colorblind. A university’s introductory psychology course is taught in a large lecture hall. Among the students there are $325$ males. Thus, the mean and the standard deviation will be calculated as:

  $\begin{array}{l}\text{Mean}=np\\ =325\times 0.08\\ =26\\ \text{Standard deviation}=\sqrt{npq}\\ =\sqrt{325\times 0.08\times 0.92}\\ =4.891\\ \approx 4.9\end{array}$

(c)

To determine

To sketch the sampling model, using the $68-95-99.7$ rule.

Explanation of Solution

It is given in the question that medical literature says that about $8\%$ of males are colorblind. A university’s introductory psychology course is taught in a large lecture hall. Among the students there are $325$ males. Thus, the sampling model sketch using $68-95-99.7$ rule is as:

  

(d)

To determine

To write a few sentences explaining what the model says about this professor’s class.

Explanation of Solution

It is given in the question that medical literature says that about $8\%$ of males are colorblind. A university’s introductory psychology course is taught in a large lecture hall. Among the students there are $325$ males. Thus, the model says about this that $68\%$ of the classes will have between $21.1\text{ to 30}\text{.9}$ colorblind people. $99.7\%$ of classes will have between $11.3\text{ and 40}\text{.7}$ colorblind people.