Section 6.8 Normal Approximation of the Binomial

a. Table 2 on page 807-p809 may be used for finding exact probability for binomial distribution

1. Identify the column to be used by p value and

2. identify the block to be used by n value

For example, n=10, p=0.5, find exact probability.

You need the block on page 808 for p=0.5 and n=10. Sum all the numbers 0.001+0.010+0.044+0.117+0.205 +0.246 on the table

b. Normal approximation

1. Normal distribution is a continuous distribution

2. Binomial distribution is a discrete distribution

3. It needs correction for continuity for Normal approximation to binomial

Rule says: The normal approximation to a binomial distribution is appropriate if np and n(1-p) both equal or exceed 5

c. Procedure for normal approximation

i. Correction for continuity:

1. Starting with inequality which has equal sign

2. Adding 0.5 to an upper bound

3. Subtract 0.5 from a lower bound

,

Where and are non-negative integers

ii. Find the standard score for upper bound and/or lower bound

iii. Then use Table 3 normal curve table to find the corresponding probability

For example, Use normal approximation to a binomial distribution with

Since np and n(1-p) are equal or exceed 5, the approximation is appropriate

Using normal approximation to Find

Change as and correction for continuity to be

Use Table 3,