Applying Binomial Distributions to Real-World Decisions Quiz

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| Questions: 20 | Updated: Nov 10, 2025
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1) What is the probability that exactly 2 of the 10 bulbs are defective?

Explanation

Use the binomial formula: C(10,2)(0.15)²(0.85)⁸ = 0.276

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About This Quiz
Applying Binomial Distributions To Real-world Decisions Quiz - Quiz

This final quiz challenges you to apply your knowledge of binomial distributions to solve real-world problems. Whether it’s quality control in manufacturing, sales performance in customer service, or predicting outcomes in medical testing, you'll calculate probabilities and make decisions based on binomial distributions. You’ll also determine how many trials o... see moresuccesses are needed to meet specific goals or probabilities, making the quiz a practical application of binomial probability. see less

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2) What is the expected number of defective bulbs in the sample of 10?

Explanation

Mean = n × p = 10 × 0.15 = 1.5

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3) What is the probability that at least 1 bulb is defective?

Explanation

P(at least 1) = 1 − (0.85)¹⁰ = 0.803

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4) If the manager wants to be 90% confident that she finds at least one defective bulb, approximately how many bulbs should she test?

Explanation

1 − (0.85)ⁿ ≥ 0.9 → n ≈ 15

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5) What is the probability she makes exactly 6 free throws out of 8?

Explanation

P = C(8,6)(0.75)⁶(0.25)² = 0.311

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6) What is the probability the medicine works for all 12 patients?

Explanation

P = (0.8)¹² = 0.069

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7) What is the probability the student gets exactly 3 correct answers?

Explanation

P = C(5,3)(0.25)³(0.75)² = 0.088

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8) What is the probability that exactly 6 customers prefer Brand A?

Explanation

P = C(15,6)(0.4)⁶(0.6)⁹ = 0.207

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9) What is the most likely number of customers who prefer Brand A?

Explanation

Mode = (n + 1)p = 16 × 0.4 = 6.4 → 6

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10) What is the probability that fewer than 4 customers prefer Brand A?

Explanation

Add P(0) + P(1) + P(2) + P(3) = 0.091

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11) Is the probability of at least 5 customers preferring Brand A more than 50%?

Explanation

P(X ≥ 5) = 1 − P(X ≤ 4) = 0.783 > 0.5

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12) What is the probability that exactly 1 passenger does not show up?

Explanation

P = C(20,1)(0.05)(0.95)¹⁹ = 0.189

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13) What is the expected number of defective chips?

Explanation

Mean = n × p = 50 × 0.02 = 1.0

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14) What is the probability that exactly 15 voters support the candidate?

Explanation

P = C(25,15)(0.55)¹⁵(0.45)¹⁰ = 0.142

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15) What is the probability that more than 18 voters support the candidate?

Explanation

Add probabilities for X = 19 to 25 → 0.026

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16) Which statement best describes the expected outcome?

Explanation

Mean = n × p = 25 × 0.55 = 13.75 → about 13–14

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17) What is the probability that at least 5 calls result in sales?

Explanation

P(X ≥ 5) = 1 − P(X ≤ 4) ≈ 0.150

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18) What is the probability of getting exactly 10 heads?

Explanation

P = C(20,10)/2²⁰ = 0.176

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19) What is the probability that the test correctly identifies at least 7 of 8 patients?

Explanation

P(≥7) = C(8,7)(0.9)⁷(0.1) + (0.9)⁸ = 0.813

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20) What is the standard deviation of the number of no-shows?

Explanation

SD = √(n × p × (1 − p)) = √(30 × 0.2 × 0.8) = 2.19

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What is the probability that exactly 2 of the 10 bulbs are defective?
What is the expected number of defective bulbs in the sample of 10?
What is the probability that at least 1 bulb is defective?
If the manager wants to be 90% confident that she finds at least one...
What is the probability she makes exactly 6 free throws out of 8?
What is the probability the medicine works for all 12 patients?
What is the probability the student gets exactly 3 correct answers?
What is the probability that exactly 6 customers prefer Brand A?
What is the most likely number of customers who prefer Brand A?
What is the probability that fewer than 4 customers prefer Brand A?
Is the probability of at least 5 customers preferring Brand A more...
What is the probability that exactly 1 passenger does not show up?
What is the expected number of defective chips?
What is the probability that exactly 15 voters support the candidate?
What is the probability that more than 18 voters support the...
Which statement best describes the expected outcome?
What is the probability that at least 5 calls result in sales?
What is the probability of getting exactly 10 heads?
What is the probability that the test correctly identifies at least 7...
What is the standard deviation of the number of no-shows?
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