lOMoAR cPSD| 61371432
WGU C955 Applied Probability & Stats: Comprehensive
Study Notes | Complete study set with Solutions | 2026
Updates | 100% correct
Module 1:
Whole numbers: These are numbers like 1, 2, 3, etc., that are complete or "whole." They
have no fractional or decimal parts. For example, 1 and 2 are whole numbers because
they don't include any parts like 1/2 or 0.75. Importantly, whole numbers are non-
negative, meaning they start at 0 and go up from there (0, 1, 2, 3...). Fractions and
Decimals represent parts of a whole number. A fraction like "1/2" or a decimal like "0.5"
expresses a value that is less than 1 and represents a portion or part of something.
Integers: Like whole numbers, these numerical figures that do not contain a fractional or
decimal component. Unlike whole numbers, it can be either a positive number (1), a
negative number (-2), or zero. Whole numbers are different than integers!
Positive and negative integers: Positive integers are greater than zero and appear to the
right of 0 on the number line, while negative integers are less than zero and appear to the
left of the number line. Zero is neither positive nor negative but is considered an integer.
Positive integers include 1, 2, 3, etc., and negative integers, like -1, -2, -3, are shown with
a minus sign.
Rational numbers: Rational numbers are numbers that can be expressed as fractions,
including all integers (e.g., 4 = 4/1). They also include decimals that either terminate or
, lOMoAR cPSD| 61371432
repeat indefinitely, such as -310/1, which equals -0.02970297... or 0.0297⎯⎯ (the line is
over 0297) (where 0297 repeats forever).
Real numbers: Any numbers on the number line. Real numbers include zero, negative and
positive integers, rational numbers, and even numbers that are not rational (such as π).
Applying negative numbers to personal finance: Negative numbers in finance represent
amounts owed, indicating a balance less than $0, or debt. For example, if Alison has a
bank balance of $1,200 and withdraws $1,300, her new balance becomes $1,200 - $1,300,
resulting in -$100. This negative amount means she owes the bank $100, which would be
to the left of the number line. This is referred to as an overdraft, reflecting that her
account is overdrawn.
Applying negative numbers to temperature: Various scales measure temperature,
including Kelvin, Celsius, and Fahrenheit, with Fahrenheit (°F) being the most common
in the United States. Negative numbers on this scale indicate temperatures below 0°F. For
instance, if the temperature in Minneapolis is 5°F and drops by 8°F, the new temperature
becomes 5°F - 8°F, resulting in -3°F, which is to the left of 0 on the number line. This
indicating it is now colder than 0°F.
Negative numbers: When dealing with negative numbers, the logic is reversed compared
to positive numbers. For example, owing $40 is better than owing $50 because -40 is
greater than -50. On a number line, numbers to the right are always greater, so while 5 is
greater than 3, 0 is greater than -3, and -3 is greater than -5. This visual helps compare
values and understand which numbers are larger or smaller.
, lOMoAR cPSD| 61371432
Whole numbers and integers on a number line: Whole numbers, like 16, 1, 3024, and 5,
can be arranged from least to greatest: 1, 5, 16, 3024, following the concept of a number
line where values increase as you move right. For negative integers, the farther left from
zero, the smaller the value, such as -3 being less than 2 on the number line.
−3 is less than 2 and should be placed to the left of 2.
Rational numbers on a number line: To place a rational number on the number line,
recognize that any fraction or decimal makes the number greater than its whole number
part. For example, 4.3 is placed between 4 and 5, not between 3 and 4, and 1.34 is placed
between 1 and 2, and ¾ will be a little behind 2 on the number line.
Negative fractions and decimals on a number line: Negative fractions and decimals can
be placed between negative integers the same way, though remember that the lesser value
integer will be to the left of the greater integer. For negative numbers, the farther away
from zero, the smaller the value.
, lOMoAR cPSD| 61371432
Data that can be discrete and continuous: In mathematics, a group of numbers is called a
set, and in statistics, it's often referred to as data. These groups can be either discrete, with
distinct and separate values, or continuous, where the values are connected without gaps.
Discrdete data sets: Discrete sets consist of distinct, countable values with gaps between
them. In mathematics, whole numbers and integers are examples of discrete sets. In
statistics, discrete data sets include things like the number of adults in a household, dice
roll outcomes, and the number of machines in operation, as these values are separate and
unconnected.
Continuous data sets: Continuous sets can take any value within an interval and are
measured rather than counted, with no clear boundaries between elements. In
mathematics, the set of real numbers is continuous, like a number line with no gaps. In
statistics, continuous data sets include things like temperature, distance, and time, where
values can be any real number within a certain range.
Distribution sets: An entire set of data can also be categorized as discrete or continuous. If
a distribution* turns out to have a defined number of outcomes, the distribution is
considered discrete. If the distribution results in any number of outcomes in an interval, it
is considered continuous.
Intervals and sets (greater or less than inewuality symbol): Both discrete and continuous
data form sets, a collection of numbers, and different notations indicate the type of data
and included values. Symbols like "<" mean "less than," and ">" means "greater than,"
with the open side always pointing to the larger quantity. For example, "5 > 3" is
WGU C955 Applied Probability & Stats: Comprehensive
Study Notes | Complete study set with Solutions | 2026
Updates | 100% correct
Module 1:
Whole numbers: These are numbers like 1, 2, 3, etc., that are complete or "whole." They
have no fractional or decimal parts. For example, 1 and 2 are whole numbers because
they don't include any parts like 1/2 or 0.75. Importantly, whole numbers are non-
negative, meaning they start at 0 and go up from there (0, 1, 2, 3...). Fractions and
Decimals represent parts of a whole number. A fraction like "1/2" or a decimal like "0.5"
expresses a value that is less than 1 and represents a portion or part of something.
Integers: Like whole numbers, these numerical figures that do not contain a fractional or
decimal component. Unlike whole numbers, it can be either a positive number (1), a
negative number (-2), or zero. Whole numbers are different than integers!
Positive and negative integers: Positive integers are greater than zero and appear to the
right of 0 on the number line, while negative integers are less than zero and appear to the
left of the number line. Zero is neither positive nor negative but is considered an integer.
Positive integers include 1, 2, 3, etc., and negative integers, like -1, -2, -3, are shown with
a minus sign.
Rational numbers: Rational numbers are numbers that can be expressed as fractions,
including all integers (e.g., 4 = 4/1). They also include decimals that either terminate or
, lOMoAR cPSD| 61371432
repeat indefinitely, such as -310/1, which equals -0.02970297... or 0.0297⎯⎯ (the line is
over 0297) (where 0297 repeats forever).
Real numbers: Any numbers on the number line. Real numbers include zero, negative and
positive integers, rational numbers, and even numbers that are not rational (such as π).
Applying negative numbers to personal finance: Negative numbers in finance represent
amounts owed, indicating a balance less than $0, or debt. For example, if Alison has a
bank balance of $1,200 and withdraws $1,300, her new balance becomes $1,200 - $1,300,
resulting in -$100. This negative amount means she owes the bank $100, which would be
to the left of the number line. This is referred to as an overdraft, reflecting that her
account is overdrawn.
Applying negative numbers to temperature: Various scales measure temperature,
including Kelvin, Celsius, and Fahrenheit, with Fahrenheit (°F) being the most common
in the United States. Negative numbers on this scale indicate temperatures below 0°F. For
instance, if the temperature in Minneapolis is 5°F and drops by 8°F, the new temperature
becomes 5°F - 8°F, resulting in -3°F, which is to the left of 0 on the number line. This
indicating it is now colder than 0°F.
Negative numbers: When dealing with negative numbers, the logic is reversed compared
to positive numbers. For example, owing $40 is better than owing $50 because -40 is
greater than -50. On a number line, numbers to the right are always greater, so while 5 is
greater than 3, 0 is greater than -3, and -3 is greater than -5. This visual helps compare
values and understand which numbers are larger or smaller.
, lOMoAR cPSD| 61371432
Whole numbers and integers on a number line: Whole numbers, like 16, 1, 3024, and 5,
can be arranged from least to greatest: 1, 5, 16, 3024, following the concept of a number
line where values increase as you move right. For negative integers, the farther left from
zero, the smaller the value, such as -3 being less than 2 on the number line.
−3 is less than 2 and should be placed to the left of 2.
Rational numbers on a number line: To place a rational number on the number line,
recognize that any fraction or decimal makes the number greater than its whole number
part. For example, 4.3 is placed between 4 and 5, not between 3 and 4, and 1.34 is placed
between 1 and 2, and ¾ will be a little behind 2 on the number line.
Negative fractions and decimals on a number line: Negative fractions and decimals can
be placed between negative integers the same way, though remember that the lesser value
integer will be to the left of the greater integer. For negative numbers, the farther away
from zero, the smaller the value.
, lOMoAR cPSD| 61371432
Data that can be discrete and continuous: In mathematics, a group of numbers is called a
set, and in statistics, it's often referred to as data. These groups can be either discrete, with
distinct and separate values, or continuous, where the values are connected without gaps.
Discrdete data sets: Discrete sets consist of distinct, countable values with gaps between
them. In mathematics, whole numbers and integers are examples of discrete sets. In
statistics, discrete data sets include things like the number of adults in a household, dice
roll outcomes, and the number of machines in operation, as these values are separate and
unconnected.
Continuous data sets: Continuous sets can take any value within an interval and are
measured rather than counted, with no clear boundaries between elements. In
mathematics, the set of real numbers is continuous, like a number line with no gaps. In
statistics, continuous data sets include things like temperature, distance, and time, where
values can be any real number within a certain range.
Distribution sets: An entire set of data can also be categorized as discrete or continuous. If
a distribution* turns out to have a defined number of outcomes, the distribution is
considered discrete. If the distribution results in any number of outcomes in an interval, it
is considered continuous.
Intervals and sets (greater or less than inewuality symbol): Both discrete and continuous
data form sets, a collection of numbers, and different notations indicate the type of data
and included values. Symbols like "<" mean "less than," and ">" means "greater than,"
with the open side always pointing to the larger quantity. For example, "5 > 3" is
