Find the normal approximation for the binomial probability P

Find the normal approximation for the binomial probability P(x

Solution

We need to use the continuity correction factor on the X value.

Step 1: Work out np and nq:
np = 14 * 0.4 = 5.6 (note: this is also the mean of the binomial distribution)
nq = 14 * 0.6 = 8.4
These are both over 5, so we can use the continuity correction factor.

Step 2: Figure out the variance of the binomial distribution:
n*p*q = 14*0.4*0.6 = 3.36
Set this number aside for a moment.

Step 3: Use the continuity correction factor on the X value.
X 8 becomes X (8+0.5) so X 8.5 .

Step 4: Find the z-score
z = 8.5 – 5.6 / 3.36 = 1.58

Step 5: Look up Step 4 in the z-table
1.29 = .9429.
The probability that X 8 is 0.9429.