πΉ Definition: The BINOM.DIST
function in Microsoft Excel calculates the individual term binomial distribution probability.
πΉ Purpose: It’s used to determine the probability of obtaining a specific number of successes in a fixed number of trials, given a fixed probability of success on each trial.
πΉ Syntax & Arguments:
BINOM.DIST(number_s, trials, probability_s, cumulative)
πΉ Explain the Arguments in the function:
number_s
: The number of successes in trials.trials
: The number of independent trials.probability_s
: The probability of success on each trial.cumulative
: A logical value; TRUE returns the cumulative distribution function; FALSE returns the probability mass function.
πΉ Return value: This function returns the binomial distribution probability.
πΉ Remarks: Ensure that the values provided for trials and number_s are integers, and the probability_s lies between 0 and 1.
Part 2: Examples
π Example 1:
β’ Purpose of example: Determine the probability of 2 products being defective out of a sample of 5, given a 10% defect rate.
β’ Data tables and formulas:
A | B | C | D | |
---|---|---|---|---|
1 | Number_s | Trials | Prob | Result |
2 | 2 | 5 | 0.10 | =BINOM.DIST(A2,B2,C2,FALSE) |
3 | 0.072 |
β’ Explanation: Given a 10% defect rate, the probability of finding exactly 2 defective products in a sample of 5 is 7.2%.
π Example 2:
β’ Purpose of example: Determine the cumulative probability of selling up to 3 products on a given day, given a 25% success rate.
β’ Data tables and formulas:
A | B | C | D | |
---|---|---|---|---|
1 | Number_s | Trials | Prob | Result |
2 | 3 | 10 | 0.25 | =BINOM.DIST(A2,B2,C2,TRUE) |
3 | 0.888 |
β’ Explanation: Given a 25% success rate, the cumulative probability of selling up to 3 products in 10 attempts is 88.8%.
π Example 3:
β’ Purpose of example: Determine the probability of a salesperson making exactly 5 sales out of 20 pitches, given a 20% success rate.
β’ Data tables and formulas:
A | B | C | D | |
---|---|---|---|---|
1 | Number_s | Trials | Prob | Result |
2 | 5 | 20 | 0.20 | =BINOM.DIST(A2,B2,C2,FALSE) |
3 | 0.174 |
β’ Explanation: Given a 20% success rate, the probability of a salesperson making exactly 5 sales out of 20 pitches is 17.4%.
π Example 4:
β’ Purpose of example: Determine the cumulative probability of a factory producing up to 4 defective items in a batch of 50, given a 5% defect rate.
β’ Data tables and formulas:
A | B | C | D | |
---|---|---|---|---|
1 | Number_s | Trials | Prob | Result |
2 | 4 | 50 | 0.05 | =BINOM.DIST(A2,B2,C2,TRUE) |
3 | 0.216 |
β’ Explanation: Given a 5% defect rate, the cumulative probability of the factory producing up to 4 defective items in a batch of 50 is 21.6%.
π Example 5:
β’ Purpose of example: Determine the probability of a call center receiving exactly 10 complaints daily with 200 calls, given a 3% complaint rate.
β’ Data tables and formulas:
A | B | C | D | |
---|---|---|---|---|
1 | Number_s | Trials | Prob | Result |
2 | 10 | 200 | 0.03 | =BINOM.DIST(A2,B2,C2,FALSE) |
3 | 0.057 |
β’ Explanation: Given a 3% complaint rate, the probability of the call center receiving exactly 10 complaints out of 200 calls is 5.7%.
π Example 6: Using BINOM.DIST with IF
β’ Purpose of example: Determine if a batch of 100 products with 7 defects is within acceptable quality limits, given a 5% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 7 | 100 | 0.05 | =IF(BINOM.DIST(A2,B2,C2,TRUE)<0.95, “Acceptable”, “Not Acceptable”) | Acceptable |
β’ Explanation: The cumulative probability of finding up to 7 defects in a batch of 100 is checked against a 95% quality threshold. If it’s below 95%, the batch is deemed acceptable. In this case, the batch is within acceptable limits.
π Example 7: Using BINOM.DIST with SUM
β’ Purpose of example: Calculate the probability of having 2, 3, or 4 defective items in a batch of 50, given a 4% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 2 | 50 | 0.04 | =SUM(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE)) | 0.207 |
3 | 3 | 50 | 0.04 | ||
4 | 4 | 50 | 0.04 |
β’ Explanation: The individual probabilities of having 2, 3, or 4 defective items are summed up to get a combined probability. In this scenario, there’s a 20.7% chance of having 2 to 4 defective items in a batch of 50.
π Example 8: Using BINOM.DIST with VLOOKUP
β’ Purpose of example: Given a table of defect rates, determine the probability of 3 defects in a batch of 40 for a specific product type.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Product Type | Number_s | Trials | Formula | Result |
2 | Type A | 3 | 40 | =BINOM.DIST(B2,C2,VLOOKUP(A2,F:G,2,FALSE),FALSE) | 0.061 |
3 |
Defect Rates Table:
F | G | |
---|---|---|
1 | Product Type | Defect Rate |
2 | Type A | 0.05 |
3 | Type B | 0.07 |
β’ Explanation: The VLOOKUP
function fetches the “Type A” defect rate from the Defect Rates Table. The BINOM.DIST
function then calculates the probability of having 3 defects in a batch of 40 for “Type A”. The result is a 6.1% chance.
π Example 9: Using BINOM.DIST with AVERAGE
β’ Purpose of example: Calculate the average probability of having 1, 2, or 3 defects in three batches of 30 products, given a 6% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 1 | 30 | 0.06 | =AVERAGE(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE)) | 0.165 |
3 | 2 | 30 | 0.06 | ||
4 | 3 | 30 | 0.06 |
β’ Explanation: The individual probabilities of having 1, 2, or 3 defects are averaged to provide a mean probability across the three scenarios. The average probability of having 1 to 3 defects in a batch of 30 products, given a 6% defect rate, is 16.5%.
π Example 10: Using BINOM.DIST with MAX
β’ Purpose of example: Determine the highest probability of defects among 1, 2, or 3 faults in a batch of 40 products, given a 5% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 1 | 40 | 0.05 | =MAX(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE)) | 0.184 |
3 | 2 | 40 | 0.05 | ||
4 | 3 | 40 | 0.05 |
β’ Explanation: The MAX
function is used to determine the highest probability among the three scenarios. The highest probability is having just 1 defect in a batch of 40 products, which is 18.4%.
π Example 11: Using BINOM.DIST with MIN
β’ Purpose of example: Determine the lowest probability of defects among 1, 2, or 3 faults in a batch of 50 products, given a 4% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 1 | 50 | 0.04 | =MIN(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE)) | 0.020 |
3 | 2 | 50 | 0.04 | ||
4 | 3 | 50 | 0.04 |
β’ Explanation: The MIN
function is used to determine the lowest probability among the three scenarios. The lowest probability is 3 defects in a batch of 50 products, which is 2.0%.
π Example 12: Using BINOM.DIST with ROUND
β’ Purpose of example: Calculate the rounded probability of having 4 defects in a batch of 60 products, given a 3% defect rate.
β’ Data tables and formulas:
A | B | C | D | E | |
---|---|---|---|---|---|
1 | Number_s | Trials | Prob | Formula | Result |
2 | 4 | 60 | 0.03 | =ROUND(BINOM.DIST(A2,B2,C2,FALSE), 3) | 0.167 |
β’ Explanation: The ROUND
function is used to round the result of the BINOM.DIST
function to three decimal places. The rounded probability of having 4 defects in a batch of 60 products, given a 3% defect rate, is 16.7%.
Part 3: Tips and tricks:
- π Ensure that the
probability_s
value is between 0 and 1. Any value outside this range will result in an error. - π If you’re looking for the probability of getting more than a certain number of successes, subtract the cumulative probability from 1.
- π Remember that the
BINOM.DIST
function assumes that each trial is independent of the others. - π For large datasets, consider using the
BINOM.DIST.RANGE
function to compute probabilities over a range of values.