Statistics 101: Principles of Statistics
Study.com1Ultimate 2026–2027 Exam Prep
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Description
The Ultimate 2026–2027 Exam Prep Bundle
is a complete and carefully structured study
resource designed to help students prepare
effectively, strengthen understanding, and
improve performance through targeted practice
and clear, guided explanations.
This guide is built to support both independent
learning and focused revision, offering a
balanced combination of exam-style questions,
fully worked solutions, and simplified
concept breakdowns. It is ideal for students
who want to move beyond memorization and
,develop the ability to analyze, interpret, and
solve exam questions with confidence.
Graph of Z-Scores - ANSWER✅Normally distributed data Mean = 0 (if z-score = 0,
then data point = mean) Standard deviation = 1
Graph of Z-Scores - ANSWER✅Normally distributed data Mean = 0 (if z-score = 0,
then data point = mean) Standard deviation = 1
Empirical Rule
(68-95-99.7 Rule) - ANSWER✅For normally distributed data:
--68% of data within 1 standard deviation
of the mean.
--95% of data within 2 standard deviations
of the mean.
--99.7% of data within 3 standard deviations
of the mean.
Continuous Probability Distribution - ANSWER✅You use this process model when
dealing with a number of possible
outcomes that you cannot count. If you
can count outcomes, you should use
discrete probability distribution
The average life span of tabby cats is 18 years with a standard deviation of 2.
Determine the percentage of tabby cats that will live longer than 22 years -
ANSWER✅Z-score for 20 years: (22 - 18) / 2 = 2
2.0 on table: 0.97725
Subtract from 1 to find percent greater
(to the right): 1 - 0.97725 = 0.02275 =
2.275%
The average tail length of tabby cats is 12.5 inches with a standard deviation of 0.5.
Determine the number of tabby cats that will have a tailless than than 11 inches in a
population of 1,000 - ANSWER✅Z-score for 11 inches: (11 - 12.5) / 0.5 = -3
-3.0 on table: 0.00135
0.00135 x 1000 = 1.35 = 1 cat
Characteristics & Example
Determining the Area Between Two Z-Scores - ANSWER✅1. Locate z-scores on 'Z-
Scores and Normal Curve Areas' table
, 2. Subtract values by 0.500 if table measures from 0 (if area for 1 = 0.8413)
3. Subtract larger z-score area by smaller z-score area
How to use the normal distribution to approximate binomial distribution - ANSWER✅n
= number of trials, p = probability of success
Mean = np
Standard deviation = √(np(1-p))
To solve: calculate z-score(s), find value(s) on normal distribution table, calculate
probability
Graph of Normal Distribution - ANSWER✅Graph using the normal distribution to
approximate the binomial distribution
Calculate the probability of getting at least 12 heads when flipping a fair coin 40 times -
ANSWER✅Calculate the probability of getting at least 12 heads when flipping a fair
coin 40 times,
Mean = np = 40 x 0.5 = 20
Standard deviation = √(40 x 0.5 x (1 -0.5)) = 3.2
Z-score of 12: (12 - 20) / 3.2 = -2.5 -2.5 on table: 0.0062
1 - 0.0062 = 0.9938 = 99%
Z-Score - ANSWER✅This describes the number of standard deviations a data point is
from the mean. It's useful for quickly and accurately determining normal distribution
probabilities
Calculating the Z-Score - ANSWER✅1. Subtract the data point by the mean.
2. Divide the difference by the standard deviation.
If result is negative it is to the left of the mean on the graph of normal distribution
Find the area that falls between z = 1 and z = -1 - ANSWER✅1. z = 1: 0.84134 z = -1:
0.15866
2. 0.84134 - 0.500 = 0.34134 0.15866 -
0.500 = -0.34134
3. 0.34134 - -0.34134 = 0.68268
The average whisker length of tabby
cats is 4.4 inches with a standard
deviation of 0.2. Determine the
percentage of cats with a whisker
length between 4.2 and 4.8 inches,
Z-score for 4.2 inches: (4.2 - 4.4) / 0.2 = -1
Study.com1Ultimate 2026–2027 Exam Prep
Bundle: Updated Question Bank, Fully
Worked Solutions, Concept Breakdown &
Smart Revision Techniques
Description
The Ultimate 2026–2027 Exam Prep Bundle
is a complete and carefully structured study
resource designed to help students prepare
effectively, strengthen understanding, and
improve performance through targeted practice
and clear, guided explanations.
This guide is built to support both independent
learning and focused revision, offering a
balanced combination of exam-style questions,
fully worked solutions, and simplified
concept breakdowns. It is ideal for students
who want to move beyond memorization and
,develop the ability to analyze, interpret, and
solve exam questions with confidence.
Graph of Z-Scores - ANSWER✅Normally distributed data Mean = 0 (if z-score = 0,
then data point = mean) Standard deviation = 1
Graph of Z-Scores - ANSWER✅Normally distributed data Mean = 0 (if z-score = 0,
then data point = mean) Standard deviation = 1
Empirical Rule
(68-95-99.7 Rule) - ANSWER✅For normally distributed data:
--68% of data within 1 standard deviation
of the mean.
--95% of data within 2 standard deviations
of the mean.
--99.7% of data within 3 standard deviations
of the mean.
Continuous Probability Distribution - ANSWER✅You use this process model when
dealing with a number of possible
outcomes that you cannot count. If you
can count outcomes, you should use
discrete probability distribution
The average life span of tabby cats is 18 years with a standard deviation of 2.
Determine the percentage of tabby cats that will live longer than 22 years -
ANSWER✅Z-score for 20 years: (22 - 18) / 2 = 2
2.0 on table: 0.97725
Subtract from 1 to find percent greater
(to the right): 1 - 0.97725 = 0.02275 =
2.275%
The average tail length of tabby cats is 12.5 inches with a standard deviation of 0.5.
Determine the number of tabby cats that will have a tailless than than 11 inches in a
population of 1,000 - ANSWER✅Z-score for 11 inches: (11 - 12.5) / 0.5 = -3
-3.0 on table: 0.00135
0.00135 x 1000 = 1.35 = 1 cat
Characteristics & Example
Determining the Area Between Two Z-Scores - ANSWER✅1. Locate z-scores on 'Z-
Scores and Normal Curve Areas' table
, 2. Subtract values by 0.500 if table measures from 0 (if area for 1 = 0.8413)
3. Subtract larger z-score area by smaller z-score area
How to use the normal distribution to approximate binomial distribution - ANSWER✅n
= number of trials, p = probability of success
Mean = np
Standard deviation = √(np(1-p))
To solve: calculate z-score(s), find value(s) on normal distribution table, calculate
probability
Graph of Normal Distribution - ANSWER✅Graph using the normal distribution to
approximate the binomial distribution
Calculate the probability of getting at least 12 heads when flipping a fair coin 40 times -
ANSWER✅Calculate the probability of getting at least 12 heads when flipping a fair
coin 40 times,
Mean = np = 40 x 0.5 = 20
Standard deviation = √(40 x 0.5 x (1 -0.5)) = 3.2
Z-score of 12: (12 - 20) / 3.2 = -2.5 -2.5 on table: 0.0062
1 - 0.0062 = 0.9938 = 99%
Z-Score - ANSWER✅This describes the number of standard deviations a data point is
from the mean. It's useful for quickly and accurately determining normal distribution
probabilities
Calculating the Z-Score - ANSWER✅1. Subtract the data point by the mean.
2. Divide the difference by the standard deviation.
If result is negative it is to the left of the mean on the graph of normal distribution
Find the area that falls between z = 1 and z = -1 - ANSWER✅1. z = 1: 0.84134 z = -1:
0.15866
2. 0.84134 - 0.500 = 0.34134 0.15866 -
0.500 = -0.34134
3. 0.34134 - -0.34134 = 0.68268
The average whisker length of tabby
cats is 4.4 inches with a standard
deviation of 0.2. Determine the
percentage of cats with a whisker
length between 4.2 and 4.8 inches,
Z-score for 4.2 inches: (4.2 - 4.4) / 0.2 = -1
