Z SCORE TABLE
  • Z Table
    • Z Scores to Percentiles Chart
    • Z Score Calculator
    • Z Score Probability Calculator
    • Interactive Z Table
    • Z Score Formula
    • How to calculate the z score
    • How To Use Z-Score Table
    • Calculate Z-score
    • Parameters in Statistics
    • Z Score Chart Basics
    • History of Normal Distirbution
    • Statistics Z Score Jokes
    • When to Use Z Test vs T Test
    • Z Score Practice Problems
    • Confidence Interval Calculator >
      • Confidence Interval in Excel
      • 90 confidence interval z score
      • 95 Confidence Interval Z Score
      • 99 Confidence Interval Z Score
    • Z Score Confidence Interval
  • Statistics
    • Statistics Symbols
    • Statistics Formulas >
      • Binomial Coefficient
      • Empirical Rule
      • Correlation Coefficient
    • P Value Calculator >
      • P Value Calculator from Z Score
      • P Value Calculator from T Score
      • P Value Calculator from Chi-Square
      • P Value Calculator from F Ratio (ANOVA)
      • P Value Calculator from Pearson R
      • P Value Calculator Tukey's Q Score
    • Cumulative Binomial Probability Calculator
    • Interquartile Range Calculator
    • Empirical Rule Calculator
    • Mean, Median and Mode Calculator
    • Sample Size Calculator
    • Other Statistical Tables >
      • T Value Table
      • Chi-Square Table
      • F Distribution Table
    • Standard Deviation Calculator
    • Normal vs Non-Normal Distribution: Understanding the Differences
    • Explanatory Variable: Understanding Its Role in Statistical Analysis
    • Independent variable vs dependent
    • Statistics Forum
  • Math
    • Combination Calculator
    • Permutation Calculator
    • Exploring 7 Unsolvable Math Problems >
      • Riemann Hypothesis
    • Math Problems >
      • Math Problems for 1st Graders
      • Math Problems for 2nd Graders
      • Math Problems for 3rd Graders
      • Math Problems for 4th Graders
      • Math Problems for 5th Graders
      • Math Problems for 6th Graders
      • Math Problems for 7th Graders
      • Math Problems for 8th Graders
      • Math Problems for 9th Graders
      • Math Problems for 10th Graders
      • Math Problems for 11th Graders
    • Times Tables >
      • 1 Times Table
      • 2 Times Table
      • 3 Times Table
      • 4 Times Table
      • 5 Times Table
      • 6 Times Table
      • 7 Times Table
      • 8 Times Table
      • 9 Times Table
      • 10 Times Table
    • Multiplication Tables >
      • Multiplication Table by 20
      • Multiplication Table by 19
      • Multiplication Table by 18
      • Multiplication Table by 17
      • Multiplication Table by 16
      • Multiplication Table by 15
      • Multiplication Table by 14
      • Multiplication Table by 13
      • Multiplication Table by 12
      • Multiplication Table by 11
      • Multiplication Table by 10
      • Multiplication Table by 9
      • Multiplication Table by 8
      • Multiplication Table by 7
      • Multiplication Table by 6
      • Multiplication Table by 5
      • Multiplication Table by 4
      • Multiplication Table by 3
    • Roman Numerals >
      • Roman Numerals Chart
      • Roman Numerals Converter
      • I Roman Numerals
      • II Roman Numerals
      • III Roman Numerals
      • IV Roman Numerals
      • V Roman Numerals
      • VI Roman Numerals
      • VII Roman Numerals
      • VIII Roman Numerals
      • IX Roman Numerals
      • X Roman Numerals
      • XI Roman Numerals
      • XII Roman Numerals
      • XIII Roman Numerals
      • XIV Roman Numerals
      • XV Roman Numerals
      • XVI Roman Numerals
      • XVII Roman Numerals
      • XLVI Roman Numerals >
        • TEMP XVII Roman Numerals
    • Percentage Increase Calculator
    • Linear Equations >
      • Two-Variable Linear Equations Test with Answers
      • One Variable Linear Equations >
        • Ax=B Linear Equation Calculator
        • Ax=B Linear Equation Practice Test
    • Decimal Places Value Chart
    • Cone Volume Calculator
    • Rounding Calculator >
      • Round 15 to the nearest ten
      • Round 75 to the nearest ten
      • Round 35 to the nearest ten
      • Round 5 to the nearest ten
      • Round 3 to the Nearest Ten
    • Factor Calculator >
      • Factor of 36
      • Factor of 30
      • Factor of 32
      • Factor of 35
      • Factor of 39
      • Factor of 33
      • Factor of 34
      • Factor of 3
      • Factor of 3/4
      • Factor of 38
    • Radius of a Circle
    • Fraction Calculator
    • Random Number Generator
    • Horizontal Line
    • X and Y Axis
    • Root Calculator
    • Square Root Calculator >
      • Square root of 2
      • Square root of 8
      • Square root of 5
      • Square root of 4
      • Square root of 3
      • Square root of 64
      • Square root of 10
      • Square root of 16
      • Square root of 25
      • Square root of 12
      • Square root of 50
      • Square root of 20
      • Square root of 9
      • Square root of 100
      • Square root of 36
      • Square root of 6
      • Square root of 49
      • Square root of 1
      • Square root of 32
      • Square root of 40
      • Square root of 81
      • Square root of 18
      • Square root of 72
      • Square root of 13
      • Square root of 80
      • Square root of 45
    • Log Calculator
    • Inequality Symbols
    • Exponent calculator
    • Decimal to Fraction Calculator
    • Fraction to Percent Calculator
    • Scale Factor
  • Unit Conversion
    • Celsius to Fahrenheit Converter >
      • 37 C to F
    • Fahrenheit to Celsius Converter >
      • 68 F to C
    • Kilograms to Pounds Converter >
      • 60 kg to lb
      • 80 kg to lbs
      • 150 kg to lbs
      • 100 kg to lbs
      • 50 kg to lbs
    • Pounds to Kilograms Converter >
      • 1 lb to kg
      • 10 lb to kg
      • 40 lb to kg
      • 50 lb to kg
      • 60 lb to kg
      • 90 lb to kg
      • 100 lb to kg
      • 130 lb to kg
      • 150 lb to kg
    • Fluid Ounces to Milliliters
    • Kilometers to Miles Converter >
      • 1 kilometer to miles
      • 5 km to miles
      • 10 km to miles
      • 15 km to miles
      • 20 km to miles
      • 50 km to miles
      • 100 km to miles
    • Miles to Kilometers Conversion >
      • 1 mile to kilometers
      • 5 miles to km
      • 10 miles to km
      • 15 miles to km
      • 20 miles to km
    • KPH to MPH Converter >
      • 300 kph to mph
    • Millimeters to Inches Converter
    • Meters to Feet Converter >
      • 1 Meter to Feet
      • 2 Meters to Feet
      • 3 Meters to Feet
      • 5 Meters to Feet
      • 10 Meters to Feet
      • 20 Meters to Feet
      • 30 Meters to Feet
      • 50 Meters to Feet
      • 100 Meters to Feet
    • Centimeters to Inches Converter >
      • 2 cm to inches
      • 3 cm to inches
      • 5 cm to inches
      • 8 cm to inches
      • 10 cm to inches
      • 12 cm to inches
      • 14 cm to inches
      • 15 cm to inches
      • 17 cm to inches
      • 18 cm to inches
      • 20 cm to inches
      • 21 cm to inches
      • 25 cm to inches
      • 28 cm to inches
      • 30 cm to inches
      • 35 cm to inches
      • 40 cm to inches
      • 50 cm to inches
      • 60 cm to inches
      • 36 cm to inches
      • 45 cm to inches
      • 70 cm to inches
      • 80 cm to inches
      • 90 cm to inches
      • 100 cm to inches
      • 120 cm to inches
      • 150 cm to inches
  • Date & Time
    • Time Conversion Chart
    • Military Times Chart
    • Time Zone
  • Test Prep
    • SAT Practice Test Math
    • Math Practice Test HiSET
    • Acing the SAT: A Comprehensive and Actionable Study Guide
    • GMAT Practice Questions Math with Answers and Explanations
    • GMAT Math Formulas Sheet
    • Math Practice Test for GED with Answers and Explanations
    • Math Problems to Solve | Practice Test
    • Free Practice TEAS Test
    • CFA Sample Practice Questions | Level 3| Answers and Explanations
    • CFA Level 2 Practice Exam Questions
    • How to Prepare for CFA level 1: An Actionable Study Guide
    • ​GRE Practice Math Questions | Free | Answers & Explanations
    • Formulas for GRE Math Section
    • ACT Practice Test with Answers and Explanations
    • CFA Practice Questions for level 1
    • CPA Practice Questions
    • ASVAB Practice Test
    • IQ Test
    • How many hours to study for CPA
    • How to Excel in Your CPA Exams: A Comprehensive Preparation Guide
  • Blog
  • Contact Us
    • Advertise Here
    • Privacy Policy
    • Useful Calculators and Converters
  • Español
    • XVIII Roman Numerals
    • XIX Roman Numerals
    • XX Roman Numerals
    • XXI Roman Numerals
    • XXII Roman Numerals
    • XXIII Roman Numerals
    • XXIV Roman Numerals
    • XXV Roman Numerals
    • XVIII Roman Numerals
  • TEMPVIII Roman Numerals
  • Normal CDF Calculator

​Cumulative Binomial Probability Calculator

Calculate binomial probability with our online Binomial Probability Calculator. Easy to use and accurate, get instant results for your experiments and data analysis. It is a powerful tool for calculating the probability of a specific number of successes in a certain number of trials. With this calculator, you can easily determine the probability of achieving a certain number of successes in a given number of trials, making it an essential resource for those working with binomial distributions. Whether you're a student, a researcher, or simply someone who needs to calculate binomial probabilities on a regular basis, our calculator is an indispensable tool that can help you save time and get accurate results.
Cumulative Binomial Probability Calculator

Cumulative Binomial Probability Calculator




How to use the Cumulative Binomial Probability Calculator

To use the calculator, follow these steps:
  1. Enter the number of trials (n) in the first input field.
  2. Enter the probability of success (p) in the second input field.
  3. Enter the number of successes (x) in the third input field.
  4. Click on the "Calculate" button.
  5. The calculator will display the following results:
  •  P(X < x), which is the probability of getting less than x successes in n trials with a probability of success of p.
  •  P(X <= x), which is the probability of getting x or less successes in n trials with a probability of success of p.
  •  P(X > x), which is the probability of getting more than x successes in n trials with a probability of success of p.
  •  P(X >= x), which is the probability of getting x or more successes in n trials with a probability of success of p.
      6.   The calculator will also display an explanation of the results.

What is Cumulative Binomial Probability?

Cumulative Binomial Probability refers to the probability of achieving a certain number of successes or fewer in a given number of independent trials, each with the same probability of success. It is calculated using the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials. Cumulative binomial probability is useful in various fields, including biology, psychology, and finance, to name a few.
​Cumulative Binomial Probability Calculator

Calculating Cumulative Binomial Probability

Calculating the cumulative binomial probability involves two steps: first, you need to calculate the individual probabilities of achieving the desired number of successes or fewer in each trial, and then you need to sum those probabilities to get the cumulative probability. The following steps will guide you through the process of calculating the cumulative binomial probability:
Step 1: Calculate the Probability of Achieving the Desired Number of Successes or Fewer in Each Trial

Use the binomial probability formula to calculate the probability of achieving the desired number of successes or fewer in each trial. The formula is:
P(X ≤ x) = Σ(i=0 to x) (n choose i) * p^i * (1-p)^(n-i)
where P(X ≤ x) is the probability of achieving x or fewer successes, n is the total number of trials, p is the probability of success in a single trial, and (n choose i) is the binomial coefficient, which is the number of ways to choose i successes from n trials.
Step 2: Sum the Individual Probabilities to Get the Cumulative Probability

Sum the individual probabilities of achieving the desired number of successes or fewer in each trial to get the cumulative probability. For example, if you want to calculate the probability of achieving 2 or fewer successes in 5 trials with a probability of success of 0.5, you would use the binomial probability formula to calculate the probabilities of achieving 0, 1, and 2 successes in each trial, and then sum those probabilities to get the cumulative probability.

Examples

Here are a few examples of calculating cumulative binomial probability:

Calculate the probability of achieving 3 or fewer successes in 10 trials with a probability of success of 0.4.

Step 1: Calculate the probability of achieving 3 or fewer successes in each trial using the binomial probability formula:
P(X ≤ 3) = Σ(i=0 to 3) [ nCi * p^i * (1-p)^(n-i) ]
where n is the total number of trials, p is the probability of success in each trial, X is the random variable denoting the number of successes in n trials, and nCi denotes the binomial coefficient "n choose i".
For example, if we have n=10 trials and p=0.6, then the probability of achieving 3 or fewer successes in each trial is:
P(X ≤ 3) = Σ(i=0 to 3) [ 10Ci * 0.6^i * (1-0.6)^(10-i) ]
= [ 10C0 * 0.6^0 * (1-0.6)^10 ] + [ 10C1 * 0.6^1 * (1-0.6)^9 ] + [ 10C2 * 0.6^2 * (1-0.6)^8 ] + [ 10C3 * 0.6^3 * (1-0.6)^7 ]
= [ 1 * 1 * 0.6^0 * 0.4^10 ] + [ 10 * 0.6 * 0.4^9 ] + [ 45 * 0.6^2 * 0.4^8 ] + [ 120 * 0.6^3 * 0.4^7 ]
= 0.000105 + 0.001573 + 0.011153 + 0.042467
= 0.055298

Step 2: Calculate the probability of achieving 4 or more successes in each trial by subtracting the probability of achieving 3 or fewer successes from 1:
P(X ≥ 4) = 1 - P(X ≤ 3)
= 1 - 0.055298
= 0.944702

Step 3: Calculate the probability of achieving 4 or more successes in all 4 trials by taking the product of the probabilities of achieving 4 or more successes in each trial:
P(4 or more successes in all 4 trials) = (0.944702)^4
= 0.80804

Therefore, the probability of achieving 4 or more successes in all 4 trials with a probability of success of 0.6 in each trial is approximately 0.808 or 80.8%.
Visit us at z-table.com for more math and stats calculators.
Proudly powered by Weebly
  • Z Table
    • Z Scores to Percentiles Chart
    • Z Score Calculator
    • Z Score Probability Calculator
    • Interactive Z Table
    • Z Score Formula
    • How to calculate the z score
    • How To Use Z-Score Table
    • Calculate Z-score
    • Parameters in Statistics
    • Z Score Chart Basics
    • History of Normal Distirbution
    • Statistics Z Score Jokes
    • When to Use Z Test vs T Test
    • Z Score Practice Problems
    • Confidence Interval Calculator >
      • Confidence Interval in Excel
      • 90 confidence interval z score
      • 95 Confidence Interval Z Score
      • 99 Confidence Interval Z Score
    • Z Score Confidence Interval
  • Statistics
    • Statistics Symbols
    • Statistics Formulas >
      • Binomial Coefficient
      • Empirical Rule
      • Correlation Coefficient
    • P Value Calculator >
      • P Value Calculator from Z Score
      • P Value Calculator from T Score
      • P Value Calculator from Chi-Square
      • P Value Calculator from F Ratio (ANOVA)
      • P Value Calculator from Pearson R
      • P Value Calculator Tukey's Q Score
    • Cumulative Binomial Probability Calculator
    • Interquartile Range Calculator
    • Empirical Rule Calculator
    • Mean, Median and Mode Calculator
    • Sample Size Calculator
    • Other Statistical Tables >
      • T Value Table
      • Chi-Square Table
      • F Distribution Table
    • Standard Deviation Calculator
    • Normal vs Non-Normal Distribution: Understanding the Differences
    • Explanatory Variable: Understanding Its Role in Statistical Analysis
    • Independent variable vs dependent
    • Statistics Forum
  • Math
    • Combination Calculator
    • Permutation Calculator
    • Exploring 7 Unsolvable Math Problems >
      • Riemann Hypothesis
    • Math Problems >
      • Math Problems for 1st Graders
      • Math Problems for 2nd Graders
      • Math Problems for 3rd Graders
      • Math Problems for 4th Graders
      • Math Problems for 5th Graders
      • Math Problems for 6th Graders
      • Math Problems for 7th Graders
      • Math Problems for 8th Graders
      • Math Problems for 9th Graders
      • Math Problems for 10th Graders
      • Math Problems for 11th Graders
    • Times Tables >
      • 1 Times Table
      • 2 Times Table
      • 3 Times Table
      • 4 Times Table
      • 5 Times Table
      • 6 Times Table
      • 7 Times Table
      • 8 Times Table
      • 9 Times Table
      • 10 Times Table
    • Multiplication Tables >
      • Multiplication Table by 20
      • Multiplication Table by 19
      • Multiplication Table by 18
      • Multiplication Table by 17
      • Multiplication Table by 16
      • Multiplication Table by 15
      • Multiplication Table by 14
      • Multiplication Table by 13
      • Multiplication Table by 12
      • Multiplication Table by 11
      • Multiplication Table by 10
      • Multiplication Table by 9
      • Multiplication Table by 8
      • Multiplication Table by 7
      • Multiplication Table by 6
      • Multiplication Table by 5
      • Multiplication Table by 4
      • Multiplication Table by 3
    • Roman Numerals >
      • Roman Numerals Chart
      • Roman Numerals Converter
      • I Roman Numerals
      • II Roman Numerals
      • III Roman Numerals
      • IV Roman Numerals
      • V Roman Numerals
      • VI Roman Numerals
      • VII Roman Numerals
      • VIII Roman Numerals
      • IX Roman Numerals
      • X Roman Numerals
      • XI Roman Numerals
      • XII Roman Numerals
      • XIII Roman Numerals
      • XIV Roman Numerals
      • XV Roman Numerals
      • XVI Roman Numerals
      • XVII Roman Numerals
      • XLVI Roman Numerals >
        • TEMP XVII Roman Numerals
    • Percentage Increase Calculator
    • Linear Equations >
      • Two-Variable Linear Equations Test with Answers
      • One Variable Linear Equations >
        • Ax=B Linear Equation Calculator
        • Ax=B Linear Equation Practice Test
    • Decimal Places Value Chart
    • Cone Volume Calculator
    • Rounding Calculator >
      • Round 15 to the nearest ten
      • Round 75 to the nearest ten
      • Round 35 to the nearest ten
      • Round 5 to the nearest ten
      • Round 3 to the Nearest Ten
    • Factor Calculator >
      • Factor of 36
      • Factor of 30
      • Factor of 32
      • Factor of 35
      • Factor of 39
      • Factor of 33
      • Factor of 34
      • Factor of 3
      • Factor of 3/4
      • Factor of 38
    • Radius of a Circle
    • Fraction Calculator
    • Random Number Generator
    • Horizontal Line
    • X and Y Axis
    • Root Calculator
    • Square Root Calculator >
      • Square root of 2
      • Square root of 8
      • Square root of 5
      • Square root of 4
      • Square root of 3
      • Square root of 64
      • Square root of 10
      • Square root of 16
      • Square root of 25
      • Square root of 12
      • Square root of 50
      • Square root of 20
      • Square root of 9
      • Square root of 100
      • Square root of 36
      • Square root of 6
      • Square root of 49
      • Square root of 1
      • Square root of 32
      • Square root of 40
      • Square root of 81
      • Square root of 18
      • Square root of 72
      • Square root of 13
      • Square root of 80
      • Square root of 45
    • Log Calculator
    • Inequality Symbols
    • Exponent calculator
    • Decimal to Fraction Calculator
    • Fraction to Percent Calculator
    • Scale Factor
  • Unit Conversion
    • Celsius to Fahrenheit Converter >
      • 37 C to F
    • Fahrenheit to Celsius Converter >
      • 68 F to C
    • Kilograms to Pounds Converter >
      • 60 kg to lb
      • 80 kg to lbs
      • 150 kg to lbs
      • 100 kg to lbs
      • 50 kg to lbs
    • Pounds to Kilograms Converter >
      • 1 lb to kg
      • 10 lb to kg
      • 40 lb to kg
      • 50 lb to kg
      • 60 lb to kg
      • 90 lb to kg
      • 100 lb to kg
      • 130 lb to kg
      • 150 lb to kg
    • Fluid Ounces to Milliliters
    • Kilometers to Miles Converter >
      • 1 kilometer to miles
      • 5 km to miles
      • 10 km to miles
      • 15 km to miles
      • 20 km to miles
      • 50 km to miles
      • 100 km to miles
    • Miles to Kilometers Conversion >
      • 1 mile to kilometers
      • 5 miles to km
      • 10 miles to km
      • 15 miles to km
      • 20 miles to km
    • KPH to MPH Converter >
      • 300 kph to mph
    • Millimeters to Inches Converter
    • Meters to Feet Converter >
      • 1 Meter to Feet
      • 2 Meters to Feet
      • 3 Meters to Feet
      • 5 Meters to Feet
      • 10 Meters to Feet
      • 20 Meters to Feet
      • 30 Meters to Feet
      • 50 Meters to Feet
      • 100 Meters to Feet
    • Centimeters to Inches Converter >
      • 2 cm to inches
      • 3 cm to inches
      • 5 cm to inches
      • 8 cm to inches
      • 10 cm to inches
      • 12 cm to inches
      • 14 cm to inches
      • 15 cm to inches
      • 17 cm to inches
      • 18 cm to inches
      • 20 cm to inches
      • 21 cm to inches
      • 25 cm to inches
      • 28 cm to inches
      • 30 cm to inches
      • 35 cm to inches
      • 40 cm to inches
      • 50 cm to inches
      • 60 cm to inches
      • 36 cm to inches
      • 45 cm to inches
      • 70 cm to inches
      • 80 cm to inches
      • 90 cm to inches
      • 100 cm to inches
      • 120 cm to inches
      • 150 cm to inches
  • Date & Time
    • Time Conversion Chart
    • Military Times Chart
    • Time Zone
  • Test Prep
    • SAT Practice Test Math
    • Math Practice Test HiSET
    • Acing the SAT: A Comprehensive and Actionable Study Guide
    • GMAT Practice Questions Math with Answers and Explanations
    • GMAT Math Formulas Sheet
    • Math Practice Test for GED with Answers and Explanations
    • Math Problems to Solve | Practice Test
    • Free Practice TEAS Test
    • CFA Sample Practice Questions | Level 3| Answers and Explanations
    • CFA Level 2 Practice Exam Questions
    • How to Prepare for CFA level 1: An Actionable Study Guide
    • ​GRE Practice Math Questions | Free | Answers & Explanations
    • Formulas for GRE Math Section
    • ACT Practice Test with Answers and Explanations
    • CFA Practice Questions for level 1
    • CPA Practice Questions
    • ASVAB Practice Test
    • IQ Test
    • How many hours to study for CPA
    • How to Excel in Your CPA Exams: A Comprehensive Preparation Guide
  • Blog
  • Contact Us
    • Advertise Here
    • Privacy Policy
    • Useful Calculators and Converters
  • Español
    • XVIII Roman Numerals
    • XIX Roman Numerals
    • XX Roman Numerals
    • XXI Roman Numerals
    • XXII Roman Numerals
    • XXIII Roman Numerals
    • XXIV Roman Numerals
    • XXV Roman Numerals
    • XVIII Roman Numerals
  • TEMPVIII Roman Numerals
  • Normal CDF Calculator