Continuity Correction

Continuity Correction Since the normal distribution is for continuous data, when data has been rounded, it loses its continuity. In this case a continuity correction needs to be applied. Often the question will mention “to the nearest”

Continuity Correction Example The rainfall each year in Whakatane is normally distributed with mean=650mm and std dev = 75mm. If the rainfall is recorded to the nearest mm, find the probability that the rainfall each year is at least 740mm

740 rounded to the nearest mm means the rounded data would include values like: 738, 739, 740, 741, 742 etc To make this data take on a continuous effect we say that 740 includes all values from 739.5 up to but not including 740.5 so P(X≥740) becomes P(X>739.5) This is known as the continuity correction.

P(X≥740) = P(X>739.5) GC Lower = 739.5 Upper = 10000000 σ = 75 µ = 650 Answer = 0.11636 cc

Apply the continuity correction to: P(X>14) P(X ≥ 14) P(X<14) P(X≤14)