Question

Florida State University has $14$statistics classes scheduled for its Summer $2013$term. One class has space available for $30$students, eight classes have space for $60$students, one class has space for $70$students, and four classes have space for $100$students.

a. What is the average class size assuming each class is filled to capacity?

b. Space is available for $980$students. Suppose that each class is filled to capacity and select a statistics student at random. Let the random variable $X$equal the size of the student’s class. Define the PDF for $X$.

c. Find the mean of $X$.

d. Find the standard deviation of$X$.

Short answer

a) The number of scholars are $70$

b) The table containing variables $X$and $P\left(x\right)$

c) The typical class size and also the mean is $70$.

d) Variance is $20.702$

Step-by-step solution

Given information (part a)

The number of classes which has a space for $30$students$=1$

The number of classes which has a space for $60$students$=8$

The number of classes which has a space for $70$students$=1$

The number of classes which has a space for $100$students$=4$

Explanation (part a)

The numberof scholars:

$$\begin{gathered} =\frac{30+\left(8\times 60\right)+70+\left(4\times 100\right)}{14} \\ =70 \end{gathered}$$

Given information (part b) 

The number of classes which has a space for $30$students$=1$

The number of classes which has a space for $60$students$=8$

The number of classes which has a space for $70$students$=1$

The number of classes which has a space for $100$students$=4$

Explanation (part b)

The category length is about by variable X. Tables containing variables and likelihood are offered as

$X$	$P\left(X\right)$
$30$	$\frac{1}{14}$
$60$	$\frac{8}{14}$
$90$	$\frac{1}{14}$
$100$	$\frac{4}{14}$

Given information (part c)

The number of classes which has a space for $30$students$=1$

The number of classes which has a space for $60$students$=8$

The number of classes which has a space for $70$students$=1$

The number of classes which has a space for $100$students$=4$

Explanation (part c)

Variable X has such a method value

$$\begin{gathered} \mu =30\left(\frac{1}{14}\right)+60\left(\frac{8}{14}\right)+70\left(\frac{1}{14}\right)+100\left(\frac{4}{14}\right) \\ =70 \end{gathered}$$

Given information (part d)

The number of classes which has a space for $30$students$=1$

The number of classes which has a space for $60$students$=8$

The number of classes which has a space for $70$students$=1$

The number of classes which has a space for $100$students$=4$

Explanation (part d)

Constant X's Variance was

$$\begin{gathered} \sigma =\sqrt{\sum _x (x-\mu {)}^{2}P(x)} \\ =20.702 \end{gathered}$$