A Level Maths Notes: S2 – The Continuity Correction
The normal distribution is a continuous distribution, but it can in fact also be used to model the distribution of a discrete random variable that fits the normal distribution. We do this by introducing the continuity correction.
If we want to find the probability that a random
variable takes the value k then we find
If we want to find the probability that a random
variable takes any value less than or equal to k then we find
If we want to find the probability that a random
variable takes any value less than k then we find
Notice the difference in the above two expressions. Because X may
be equal to k in the first of these two expressions,we have
instead
of
If we want to find the probability that a random
variable takes any value greater than or equal to k then we find
If we want to find the probability that a random variable takes
any value greater than k then we find
Notice the difference in the above two expressions. Because
may
be equal to
in
the first of these two expressions,we haveinstead
of
Example: The number of worms per
of
soil is normally distributed with mean 51.4 and variance 20. Find the
probability that the number of worms in
is
60.
To find
so
To find
so
