Applying Binomial Distributions To Real-World Decisions Quiz

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

0.207

0.186

0.400

0.153

P = C(15,6)(0.4)⁶(0.6)⁹ = 0.207

Explanation

P = C(15,6)(0.4)⁶(0.6)⁹ = 0.207

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

5

6

7

8

Mode = (n + 1)p = 16 × 0.4 = 6.4 → 6

Explanation

Mode = (n + 1)p = 16 × 0.4 = 6.4 → 6

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

Yes, the probability is approximately 0.783

No, the probability is approximately 0.403

Yes, the probability is approximately 0.610

No, the probability is approximately 0.217

P(X ≥ 5) = 1 − P(X ≤ 4) = 0.783 > 0.5

Explanation

P(X ≥ 5) = 1 − P(X ≤ 4) = 0.783 > 0.5

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

0.176

0.500

0.250

0.120

P = C(20,10)/2²⁰ = 0.176

Explanation

P = C(20,10)/2²⁰ = 0.176

5) What is the probability that exactly 2 of the 10 bulbs are defective?

0.276

0.197

0.150

0.347

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

Explanation

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

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

1.0

1.5

2.0

0.15

Mean = n × p = 10 × 0.15 = 1.5

Explanation

Mean = n × p = 10 × 0.15 = 1.5

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

0.150

0.544

0.803

0.197

P(at least 1) = 1 − (0.85)¹⁰ = 0.803

Explanation

P(at least 1) = 1 − (0.85)¹⁰ = 0.803

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

10

12

14

15

1 − (0.85)ⁿ ≥ 0.9 → n ≈ 15

Explanation

1 − (0.85)ⁿ ≥ 0.9 → n ≈ 15

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

0.750

0.311

0.267

0.100

P = C(8,6)(0.75)⁶(0.25)² = 0.311

Explanation

P = C(8,6)(0.75)⁶(0.25)² = 0.311

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

0.800

0.206

0.069

0.960

P = (0.8)¹² = 0.069

Explanation

P = (0.8)¹² = 0.069

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

0.600

0.250

0.128

0.088

P = C(5,3)(0.25)³(0.75)² = 0.088

Explanation

P = C(5,3)(0.25)³(0.75)² = 0.088

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

0.091

0.127

0.217

0.186

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

Explanation

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

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

0.050

0.189

0.377

0.736

P = C(20,1)(0.05)(0.95)¹⁹ = 0.189

Explanation

P = C(20,1)(0.05)(0.95)¹⁹ = 0.189

14) What is the expected number of defective chips?

0.5

0.7

1.5

1.0

Mean = n × p = 50 × 0.02 = 1.0

Explanation

Mean = n × p = 50 × 0.02 = 1.0

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

0.550

0.142

0.172

0.096

P = C(25,15)(0.55)¹⁵(0.45)¹⁰ = 0.142

Explanation

P = C(25,15)(0.55)¹⁵(0.45)¹⁰ = 0.142

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

0.109

0.054

0.022

0.026

Add probabilities for X = 19 to 25 → 0.026

Explanation

Add probabilities for X = 19 to 25 → 0.026

17) Which statement best describes the expected outcome?

Exactly 13 or 14 voters will support the candidate

Approximately 13 to 14 voters are expected to support the candidate

At least 20 voters will support the candidate

Fewer than 10 voters will support the candidate

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

Explanation

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

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

0.300

0.527

0.150

0.103

P(X ≥ 5) = 1 − P(X ≤ 4) ≈ 0.150

Explanation

P(X ≥ 5) = 1 − P(X ≤ 4) ≈ 0.150

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

0.900

0.802

0.813

0.187

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

Explanation

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

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

2.18

6.00

4.80

2.19

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

Explanation

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

Applying Binomial Distributions to Real-World Decisions Quiz

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

2)

What first name or nickname would you like us to use?

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

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

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

5) What is the probability that exactly 2 of the 10 bulbs are defective?

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

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

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

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

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

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

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

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

14) What is the expected number of defective chips?

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

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

17) Which statement best describes the expected outcome?

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

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

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