AS/A2 Stats 1 Stats 3

S2 Topic 3: Continuous distributions
The continuity correction
When the Normal distribution (a continuous distribution) is used to find approximate answers to problems arising from the Binomial or Poisson distributions (both discrete distributions) an adjustment is made for the mismatch of types of distribution. This is called the continuity correction In each case below a probability is given. Choose the right option to show how this probability must be adjusted before the Normal distribution can be used to calculate it.

Correct:

Attempts:

% Correct:

1	P(X < 6)
	P(X £5.5)	P(X £6)	P(X £5)	P(X £6.5)
2	P(X > 6)
	P(X ³5.5)	P(X ³6)	P(X ³6.5)	P(X ³5)
3	P(2 < X < 5)
	P(2 £X £5)	P(3 £X £4)	P(2.5 £X £4.5)	P(1.5 £X £5.5)
4	P(X = 5)
	P(X =5)	P(4 £X £5)	P(5 £X £5.5)	P(4.5 £X £5.5)
5	P(X £ 8)
	P(X £7)	P(X £9)	P(X £7.5)	P(X £8.5)
6	P(X ³ 1)
	P(X ³0)	P(X ³1.5)	P(X ³0.5)	P(X ³2)
7	P(7 ³ X > 4)
	P(7.5 ³X ³4.5)	P(6.5 ³X ³4.5)	P(7.5 ³X ³3.5)	P(6.5 ³X ³3.5)
8	P(2 £ X £ 9)
	P(2.5 £X£9.5)	P(1.5 £X£9.5)	P(1.5 £X£8.5)	P(2.5 £X£8.5)
9	P(2 < X < 9)
	P(2.5 £X£9.5)	P(1.5 £X£9.5)	P(1.5 £X£8.5)	P(2.5 £X£8.5)
10	P(2 £ X < 9)
	P(2.5 £X£9.5)	P(1.5 £X£9.5)	P(1.5 £X£8.5)	P(2.5 £X£8.5)

Summary An adjustment of ±0.5 is always made when using a Normal approximation to find probabilities arising from a discrete distribution. © MathsNet 2001