# BINOM.DIST Function in Excel

🔹 Definition: The `BINOM.DIST` function in Microsoft Excel calculates the individual term binomial distribution probability.

🔹 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.

🔹 Syntax & Arguments:

syntax
```BINOM.DIST(number_s, trials, probability_s, cumulative) ```

🔹 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.

🔹 Return value: This function returns the binomial distribution probability.

🔹 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

🌟 Example 1:

Purpose of example: Determine the probability of 2 products being defective out of a sample of 5, given a 10% defect rate.

Data tables and formulas:

ABCD
1Number_sTrialsProbResult
2250.10=BINOM.DIST(A2,B2,C2,FALSE)
30.072

Explanation: Given a 10% defect rate, the probability of finding exactly 2 defective products in a sample of 5 is 7.2%.

🌟 Example 2:

Purpose of example: Determine the cumulative probability of selling up to 3 products on a given day, given a 25% success rate.

Data tables and formulas:

ABCD
1Number_sTrialsProbResult
23100.25=BINOM.DIST(A2,B2,C2,TRUE)
30.888

Explanation: Given a 25% success rate, the cumulative probability of selling up to 3 products in 10 attempts is 88.8%.

🌟 Example 3:

Purpose of example: Determine the probability of a salesperson making exactly 5 sales out of 20 pitches, given a 20% success rate.

Data tables and formulas:

ABCD
1Number_sTrialsProbResult
25200.20=BINOM.DIST(A2,B2,C2,FALSE)
30.174

Explanation: Given a 20% success rate, the probability of a salesperson making exactly 5 sales out of 20 pitches is 17.4%.

🌟 Example 4:

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.

Data tables and formulas:

ABCD
1Number_sTrialsProbResult
24500.05=BINOM.DIST(A2,B2,C2,TRUE)
30.216

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%.

🌟 Example 5:

Purpose of example: Determine the probability of a call center receiving exactly 10 complaints daily with 200 calls, given a 3% complaint rate.

Data tables and formulas:

ABCD
1Number_sTrialsProbResult
2102000.03=BINOM.DIST(A2,B2,C2,FALSE)
30.057

Explanation: Given a 3% complaint rate, the probability of the call center receiving exactly 10 complaints out of 200 calls is 5.7%.

🌟 Example 6: Using BINOM.DIST with IF

Purpose of example: Determine if a batch of 100 products with 7 defects is within acceptable quality limits, given a 5% defect rate.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
271000.05=IF(BINOM.DIST(A2,B2,C2,TRUE)<0.95, “Acceptable”, “Not Acceptable”)Acceptable

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.

🌟 Example 7: Using BINOM.DIST with SUM

Purpose of example: Calculate the probability of having 2, 3, or 4 defective items in a batch of 50, given a 4% defect rate.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
22500.04=SUM(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE))0.207
33500.04
44500.04

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.

🌟 Example 8: Using BINOM.DIST with VLOOKUP

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.

Data tables and formulas:

ABCDE
1Product TypeNumber_sTrialsFormulaResult
2Type A340=BINOM.DIST(B2,C2,VLOOKUP(A2,F:G,2,FALSE),FALSE)0.061
3

Defect Rates Table:

FG
1Product TypeDefect Rate
2Type A0.05
3Type B0.07

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.

🌟 Example 9: Using BINOM.DIST with AVERAGE

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.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
21300.06=AVERAGE(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE))0.165
32300.06
43300.06

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%.

🌟 Example 10: Using BINOM.DIST with MAX

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.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
21400.05=MAX(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE))0.184
32400.05
43400.05

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%.

🌟 Example 11: Using BINOM.DIST with MIN

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.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
21500.04=MIN(BINOM.DIST(A2,B2,C2,FALSE), BINOM.DIST(A3,B3,C3,FALSE), BINOM.DIST(A4,B4,C4,FALSE))0.020
32500.04
43500.04

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%.

🌟 Example 12: Using BINOM.DIST with ROUND

Purpose of example: Calculate the rounded probability of having 4 defects in a batch of 60 products, given a 3% defect rate.

Data tables and formulas:

ABCDE
1Number_sTrialsProbFormulaResult
24600.03=ROUND(BINOM.DIST(A2,B2,C2,FALSE), 3)0.167

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:

1. 📌 Ensure that the `probability_s` value is between 0 and 1. Any value outside this range will result in an error.
2. 📌 If you’re looking for the probability of getting more than a certain number of successes, subtract the cumulative probability from 1.
3. 📌 Remember that the `BINOM.DIST` function assumes that each trial is independent of the others.
4. 📌 For large datasets, consider using the `BINOM.DIST.RANGE` function to compute probabilities over a range of values.