July 3, 2011-Lesson on Normal Approximation to the Binomial Distribution

Days with no assignment in Stat seldom happen.

Yet, we should not be so happy ‘cause we should set up our minds ready for our next lesson, moreover assignments still can help us have sharper minds and helps us have better understanding of our lessons.

Our class started with Ms. Macatigos introducing our new lesson:  The Normal Approximation to the Binomial Distribution.

The normal distribution is often used to solve problems that involve the binomial distribution since when n is large (say, 100), the calculations are too difficult to do by hand using the binomial distribution. When p is approximately 0.5 and as n increases, the shape of the binomial distribution become similar to the normal distribution. The larger the n and the close p is to 0.5 the more similar shape of the binomial distribution is to the normal distribution.

However, when p is close to 0 or1 and n is relatively small, the normal approximation is inaccurate.

Remember: Normal approximation should be used only when (n)(p) and (n)(q) are both greater than 5.

For example if p=0.3 and n=10, (0.3)(10)=3, therefore we can’t be able to use the Normal Approximation to the Binomial Distribution in this problem because 3 is less than 5.

Here in this table the Summary of the Normal Approximation to the Binomial Distribution is shown:

These are the formulas for the mean and standard deviation to be used in normal approximation.

mean=np

standard deviation=square root of npq

  The steps for using the normal distribution to approximate the binomial distribution:

1.   Step 1:    Check to see whether the normal approximation can be used.

2.   Step 2:    Find the mean and the standard deviation.

3.   Step 3:    Write the problem in probability notation, using x.

4.   Step 4:    Rewrite the problem by using the correction for continuity correction factor, and show the corresponding area under the normal distribution.

5.    Step 5:   Find the corresponding z values.

6.    Step 6:   Find the solution.

Sample Problem:

If a baseball player’s batting average is 0.32 or 32%, find the probability that the player will get at most 26 hits in 100 times at bat.

Step by step solution for our sample problem.

By: Kent Spencer M. Mendez

                III-Gold