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.
To the Binomial Distribution
We can use the Normal Distribution to find probabilities for Binomial distributions that have large n, or when the calculations become difficult.
-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)
Summary of the Normal Approximation to the Binomial Distribution
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.
0.9656 – 0.9429 = 0.0227 So 2.27% read the paper and driveExample
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.