Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 4: Q. 80 (page 292)

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鈥檚 class. Define the PDF for $X$ .
c. Find the mean of $X$ .
d. Find the standard deviation of $X$ .

Short Answer

Expert verified

a) The number of scholars are $70$

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

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:

$= \frac{30 + (8 脳 60) + 70 + (4 脳 100)}{14} = 70$

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

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

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

$渭 = 30 (\frac{1}{14}) + 60 (\frac{8}{14}) + 70 (\frac{1}{14}) + 100 (\frac{4}{14}) = 70$

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

$蟽 = \sqrt{\underset{x}{鈭�} 鈥� (x 鈭� 渭)^{2} P (x)} = 20.702$

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Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

Given information (part c)

Explanation (part c)

Given information (part d)

Explanation (part d)

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