Download Presentation
The Normal Approximation

Loading in 2 Seconds...

1 / 10

# The Normal Approximation - PowerPoint PPT Presentation

The Normal Approximation. To the Binomial Distribution. Recall: Binomial Distributions have: 1. Fixed number of trials 2. Independent Outcomes 3. Exactly two outcomes 4. Same probabilities for each trial. Binomial Distributions.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about ' The Normal Approximation' - markku

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### The Normal Approximation

To the Binomial Distribution

Recall: Binomial Distributions have:

• 1. Fixed number of trials
• 2. Independent Outcomes
• 3. Exactly two outcomes
• 4. Same probabilities for each trial
Binomial Distributions

We can use the Normal Distribution to find probabilities for Binomial distributions that have large n, or when the calculations become difficult.

• We can only use then when n * p > 5 AND n * q >5

A correction for continuity may be used .

-a correction employed when a continuous distribution is used to approximate a discrete distribution.

-Ex. P(X) = 8 would imply having to find P(7.5<X<8.5)

• Table 6-2 on p. 342 summarizes the corrections for continuity required……

1. Check to make sure np> 5 and nq > 5

• 2. Find the mean and the standard deviation
• 3. Write the problem in probability notation, using X.
• 4. Rewrite the problem by using the continuity correction factor and show the area under the normal distribution.
• 5. Find the corresponding z-values.
• 6. Find the solution.
Steps used to approximate Binomial Distributions

6% of American Drivers read the newspaper while driving. If 300 drivers are selected at random, find the probability that exactly 25 read the newspaper while driving.

• 1. (300*.06) = 18 (300 * .94) = 282
• 2.
• 3. What P(X) are we trying to find?? P(X = 25)
• 4. Use the continuity correction…. P(24.5<X<25.5)
• 5. Find both z-values.
• = 1.58
• 6. The area between the two z-values are:

0.9656 – 0.9429 = 0.0227 So 2.27% read the paper and drive

Example

10% of members at a golf club are widowed. If 200 club members are selected at random, find the probability that exactly 10 will be widowed.

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