Binomial Bounds Worksheet Corrected
Binomial Bounds
Statistics & Probability • Worksheet
Name:
Date:
Binomial Distribution Formulas
Mean
\[\mu = np\]
Variance
\[\sigma^2 = npq\]
Standard Deviation
\[\sigma = \sqrt{npq}\]
1
A patient with tuberculosis is given a chest x-ray. Four TB x-ray specialists examined the x-ray independently. If each specialist has an 88% success rate of detecting TB when it is present, calculate the standard deviation for the number of specialists who detect the TB.
Identify \(n, p,\) and \(q\):
Calculation:
Final Answer: \(\sigma \approx\) ___________
2
A lightbulb manufacturer determines that 2% of their bulbs are defective. In a random sample of 150 lightbulbs, find the mean and standard deviation for the number of defective bulbs.
Identify \(n, p,\) and \(q\):
Calculation:
Mean: _______ Std Dev: _______
3
A basketball player has a free-throw shooting percentage of 75%. If the player takes 20 free throws during a game, what is the standard deviation of the number of successful shots?
Final Answer: \(\sigma \approx\) ___________
4
A market research firm finds that 40% of consumers in a city prefer Brand A over Brand B. If 50 consumers are randomly selected for a survey, find the variance and the standard deviation of the number of consumers who prefer Brand A.
Var: _______ Std Dev: _______
5
A student guesses on all 10 questions of a multiple-choice quiz. Each question has 4 options with only one correct answer. Calculate the standard deviation for the number of correct answers the student will get.
Final Answer: \(\sigma \approx\) ___________
Round final answers to three decimal places. © 2026
Binomial Bounds Answer Key
Binomial Bounds
Answer Key • Teacher Resource
Unit: Probability Distributions
1
TB Specialist Detection (n = 4, p = 0.88)
Variables: n = 4, p = 0.88, q = 0.12
Formula: \(\sigma = \sqrt{npq}\)
Calculation: \(\sigma = \sqrt{4 \cdot 0.88 \cdot 0.12}\)
Calculation: \(\sigma = \sqrt{0.4224}\)
Answer: \(\sigma \approx 0.650\)
2
Defective Lightbulbs (n = 150, p = 0.02)
Variables: n = 150, p = 0.02, q = 0.98
Mean: \(\mu = np = 150 \cdot 0.02 = 3.0\)
Std Dev: \(\sigma = \sqrt{150 \cdot 0.02 \cdot 0.98} = \sqrt{2.94}\)
Answer: \(\mu = 3.0\), \(\sigma \approx 1.715\)
3
Free Throw Success (n = 20, p = 0.75)
Variables: n = 20, p = 0.75, q = 0.25
Calculation: \(\sigma = \sqrt{20 \cdot 0.75 \cdot 0.25} = \sqrt{3.75}\)
Answer: \(\sigma \approx 1.936\)
4
Consumer Preference (n = 50, p = 0.40)
Variables: n = 50, p = 0.4, q = 0.6
Variance: \(\sigma^2 = npq = 50 \cdot 0.4 \cdot 0.6 = 12\)
Std Dev: \(\sigma = \sqrt{12}\)
Answer: \(\sigma^2 = 12\), \(\sigma \approx 3.464\)
5
Guessing on Quiz (n = 10, p = 0.25)
Variables: n = 10, p = 0.25, q = 0.75
Calculation: \(\sigma = \sqrt{10 \cdot 0.25 \cdot 0.75} = \sqrt{1.875}\)
Answer: \(\sigma \approx 1.369\)
Teacher Answer Key - For instructional use only.
