Continuity correction and the complete method
A binomial value is a whole bar, while a normal model is continuous. Continuity correction places the normal boundary at the edge of the included or excluded integer bar. The symbol means the normal result estimates, rather than equals, the binomial probability.
Place the boundary before or after the integer bar
event
X < 43
normal cut
42.5
z-score
0.510
43 is excluded, so cut before its bar. The gold bars are the binomial values kept by the event; the gold area is the matching normal estimate.
The graph shows the useful central window. The tiny tails continue beyond both edges and are still included in the calculated probabilities.
exact binomial ≈ 0.6967·normal with correction ≈ 0.6951
Boundary before the k bar
or uses .
Boundary after the k bar
or uses .
Key idea
Correct both ends of an integer interval
4 ≤ X ≤ 6
3
4
5
6
7
Swipe left or right to read every column →
| Binomial event | Corrected normal interval |
|---|---|
Check each end separately: include an endpoint bar by moving to its outside edge; exclude it by stopping at its inside edge.
Show the complete approximation method
- State and check and .
- Write .
- Apply the continuity correction to the event.
- Standardise with , then calculate the correct normal area.
Worked example
Fewer than 22 successes
Let . Estimate .
“Fewer than 22” excludes the 22 bar, so use 21.5.
(9709/51/O/N/25 Q5(b))
Examiner note
Let . Use a normal approximation to estimate .
Show worked answer
The 58 bar is included but the 72 bar is excluded, so use 57.5 and 71.5.