توضیح 1
At most: X<=x.
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درس 10 از 18
Translate verbal probability statements into precise inclusive integer boundaries.
Core lesson
Translate verbal probability statements into precise inclusive integer boundaries.
توضیح 1
At most: X<=x.
توضیح 2
More than: X>x.
توضیح 3
Inclusive interval: a<=X<=b.
اصطلاحات
X<=x.
No more than five late services.
X>x.
Six or more when x=5.
a<=X<=b.
Three through seven.
نمادگذاری و فرمولها
P(X>=x)=1-P(X<=x-1)
Define X, its support, parameters, units, and assumptions before substituting values.
فعالیت تعاملی
Keep integer boundaries visible when calculating tails.
P(X = x)
0.2182
F(x) = P(X <= x)
0.6296
E(X)
4
SD(X)
1.7889
| x | P(X=x) | Included in F(4) |
|---|---|---|
| 0 | 0.0115 | Yes |
| 1 | 0.0576 | Yes |
| 2 | 0.1369 | Yes |
| 3 | 0.2054 | Yes |
| 4 | 0.2182 | Yes |
| 5 | 0.1746 | No |
| 6 | 0.1091 | No |
| 7 | 0.0545 | No |
| 8 | 0.0222 | No |
| 9 | 0.0074 | No |
| 10 | 0.002 | No |
| 11 | 0.0005 | No |
| 12 | 0.0001 | No |
| 13 | 0 | No |
| 14 | 0 | No |
| 15 | 0 | No |
| 16 | 0 | No |
| 17 | 0 | No |
| 18 | 0 | No |
| 19 | 0 | No |
| 20 | 0 | No |
Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.
مثال حلشده
سناریو
Extra staff are called when at least six services are late.
P(X>5) and P(X>=5) are different.
ارتباط با R
Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.
Live R Lab
Translate exact, cumulative, interval, and upper-tail statements.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
Always display the probability statement beside the answer so the boundary is auditable.
بازاندیشی
Name the random variable, support, parameters, units, dependence assumptions, and one limitation.
دستیار
Coach me through Binomial Cumulative, Interval, and Tail Probabilities by asking about X, support, parameters, assumptions, probability notation, exact versus approximate status, and interpretation. Do not provide a quiz answer before submission or write my final capstone recommendation.
ارزیابی پایانی
منبع
Explore additional discrete-distribution explanations from properly licensed or publisher resources.
دریافتمنبع
Download an original worksheet, formula sheet, or capstone tool for this lesson.
دریافت