Activity 9
MATH 216: Statistical Thinking
Binomial Distribution Practice
Time Allocation: 15 minutes total
Part 1: Distribution Analysis (5 minutes)
Chemotherapy Success Rates:
| x (successes) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| p(x) | 0.002 | 0.029 | 0.132 | 0.309 | 0.360 | 0.168 |
Calculate:
- Mean (\(\mu\)) = _________________________
- Standard Deviation (\(\sigma\)) = ______________
Chebyshev’s Rule:
- Interval \(\mu \pm 2\sigma\) covers at least ______% of data
- Actual probability in this interval: _______________
Part 2: Binomial Formula Application (5 minutes)
Calculate: \(P(x=2)\) for \(X \sim \text{Bin}(5, 0.3)\)
Using formula: \(P(x) = \binom{n}{x} p^x q^{n-x}\)
Show work:
Result: \(P(x=2)\) = _________________________
Part 3: Binomial Properties (5 minutes)
Fitness Test Scenario:
- 10% of adults pass fitness test
- 4 adults randomly selected
- X = number who pass
Binomial Conditions Check:
- Fixed trials? □ Yes □ No
- Independence? □ Yes □ No
- Two outcomes? □ Yes □ No
- Constant probability? □ Yes □ No
Calculate: \(P(X=3)\) = _________________________
Compare Distributions:
- Bin(4, 0.1): \(\mu\) = ______, \(\sigma^2\) = ______, \(\sigma\) = ______
- Bin(40, 0.1): \(\mu\) = ______, \(\sigma^2\) = ______, \(\sigma\) = ______
- Bin(400, 0.1): \(\mu\) = ______, \(\sigma^2\) = ______, \(\sigma\) = ______