Applied Probability and Statistics
Theoretical Probability - ANSWER: Probability based on comparing the number of
possible favorable outcomes to the number of total possible outcomes
Empirical probability - ANSWER: ..., involves conducting an experiment to observe the
frequency with which an event occurs
Relative Frequency - ANSWER: A ratio that compares the frequency of each category
to the total. Number of times the event occurs/total number of Trials
Probability Formula - ANSWER: number of favorable outcomes/number of possible
outcomes
addition rule of probability - ANSWER: P(A or B) = P(A) + P(B) - P(A and B) ("or" means
add)
What is the probability that a 10-sided fair die shows a multiple of 3 or 10? - ANSWER:
2/5
You roll two six-sided dice. What is the probability of rolling a sum less than 5 or greater
than 10 - ANSWER: The answer is 1/4. There are 6 results less than 5 (rolling 1, 1; 1, 2;
1, 3; 2, 1; 2, 2; 3, 1) and 3 results greater than 10 (rolling 5, 6; 6, 5; 6, 6). The probability
is 6/36+3/36=9/36=1/4
multiplication rule for independent events (and rule) - ANSWER: P(A and B) = P(A) x
P(B)
the probability of rolling triple ones when rolling 3 dice - ANSWER: 1/6 × 1/6 × 1/6 =
1/216
Empirical Rule (68-95-99.7) Rule - ANSWER: states that, in a normal distribution, about
68% of the terms are within one standard deviation of the mean, about 95% are within
two standard deviations, and about 99.7% are within three standard deviations
Histogram (relative frequency histogram) - ANSWER: Uses adjacent bars to show the
distribution of a quantitative variable. Each bar represents the frequency (or relative
frequency) of values falling in each bin.
mean - ANSWER: average
Median - ANSWER: Middle number
, Mode - ANSWER: the most frequently occurring score(s) in a distribution
pie chart - ANSWER: A graphical display of categorical data using a "pie"; each
category is represented as a slice where the size of the slice is proportional to the
percentage of data in that category
bar chart - ANSWER: A form of graph in which numeric values are represented by
horizontal or vertical rectangles.
relative frequency - ANSWER: the fraction or percent of the time that an event occurs in
an experiment
Dot Plot - ANSWER: a graphical device that summarizes data by the number of dots
above each data value on the horizontal axis / quantitative used for smaller sets and
outliers
stem plot (also called stem and leaf plot) - ANSWER: A graphical representation of a
quantitative data set. Leading values of each data point are presented as stems and
second digits are given as leaves.
box plot - ANSWER: a graphic way of showing a summary of data using the median,
quartiles, and extremes of the data
symmetric distribution - ANSWER: the right and left sides of the histogram are
approximately mirror images of each other
skewed left - ANSWER: A skewed distribution with a tail that stretches left, toward the
smaller values.
skewed right - ANSWER: the tail to the right of the peak is longer than the tail to the left
of the peak
uniform distribution - ANSWER: the frequency of each value of the variable is evenly
spread out across the values of the variable
bimodal distribution - ANSWER: a frequency distribution having two different values that
are heavily populated with cases
multimodal - ANSWER: Describes a graph of quantitative data with more than two clear
peaks.
Scatterplots and Correlation - ANSWER: Two most common ways of describing and
quantifying association
association - ANSWER: A pattern or relationship between two variables.
Theoretical Probability - ANSWER: Probability based on comparing the number of
possible favorable outcomes to the number of total possible outcomes
Empirical probability - ANSWER: ..., involves conducting an experiment to observe the
frequency with which an event occurs
Relative Frequency - ANSWER: A ratio that compares the frequency of each category
to the total. Number of times the event occurs/total number of Trials
Probability Formula - ANSWER: number of favorable outcomes/number of possible
outcomes
addition rule of probability - ANSWER: P(A or B) = P(A) + P(B) - P(A and B) ("or" means
add)
What is the probability that a 10-sided fair die shows a multiple of 3 or 10? - ANSWER:
2/5
You roll two six-sided dice. What is the probability of rolling a sum less than 5 or greater
than 10 - ANSWER: The answer is 1/4. There are 6 results less than 5 (rolling 1, 1; 1, 2;
1, 3; 2, 1; 2, 2; 3, 1) and 3 results greater than 10 (rolling 5, 6; 6, 5; 6, 6). The probability
is 6/36+3/36=9/36=1/4
multiplication rule for independent events (and rule) - ANSWER: P(A and B) = P(A) x
P(B)
the probability of rolling triple ones when rolling 3 dice - ANSWER: 1/6 × 1/6 × 1/6 =
1/216
Empirical Rule (68-95-99.7) Rule - ANSWER: states that, in a normal distribution, about
68% of the terms are within one standard deviation of the mean, about 95% are within
two standard deviations, and about 99.7% are within three standard deviations
Histogram (relative frequency histogram) - ANSWER: Uses adjacent bars to show the
distribution of a quantitative variable. Each bar represents the frequency (or relative
frequency) of values falling in each bin.
mean - ANSWER: average
Median - ANSWER: Middle number
, Mode - ANSWER: the most frequently occurring score(s) in a distribution
pie chart - ANSWER: A graphical display of categorical data using a "pie"; each
category is represented as a slice where the size of the slice is proportional to the
percentage of data in that category
bar chart - ANSWER: A form of graph in which numeric values are represented by
horizontal or vertical rectangles.
relative frequency - ANSWER: the fraction or percent of the time that an event occurs in
an experiment
Dot Plot - ANSWER: a graphical device that summarizes data by the number of dots
above each data value on the horizontal axis / quantitative used for smaller sets and
outliers
stem plot (also called stem and leaf plot) - ANSWER: A graphical representation of a
quantitative data set. Leading values of each data point are presented as stems and
second digits are given as leaves.
box plot - ANSWER: a graphic way of showing a summary of data using the median,
quartiles, and extremes of the data
symmetric distribution - ANSWER: the right and left sides of the histogram are
approximately mirror images of each other
skewed left - ANSWER: A skewed distribution with a tail that stretches left, toward the
smaller values.
skewed right - ANSWER: the tail to the right of the peak is longer than the tail to the left
of the peak
uniform distribution - ANSWER: the frequency of each value of the variable is evenly
spread out across the values of the variable
bimodal distribution - ANSWER: a frequency distribution having two different values that
are heavily populated with cases
multimodal - ANSWER: Describes a graph of quantitative data with more than two clear
peaks.
Scatterplots and Correlation - ANSWER: Two most common ways of describing and
quantifying association
association - ANSWER: A pattern or relationship between two variables.
