1. The Normal Approximation to the Binomial Distribution
MDM 4U Lesson 5.6

2. Pascal seems normal
In the situation where the probability of success is equal to 0.5 (like flipping a coin), the binomial distribution is very close to the normal distribution

3. 20th line of Pascal's triangle
As the number of trials increases, the binomial distribution becomes smoother and more normal.

4. Difference between the Normal Distribution and Binomial Distribution
The binomial distribution represents discrete random variables
The normal distribution is continuous, which can be represented with decimals.
In order to use the normal distribution to approximate the binomial distribution, a range of values should be used, rather than the discrete values.

5. Mean and Standard deviation of the normal approximation to the binomial distribution
If X is a binomial random variable of n independent trials, each with probability of success p, and if
np > and n(1-p) > 5
then the binomial random variable can be approximated by a normal distribution.
MEAN:
Standard Deviation:

6. Example 1: Dan tosses a fair coin 50 times
Example 1: Dan tosses a fair coin 50 times. Estimate the probability that he will get tails less than 15 times.

7. Ex. 2: A soft-drink company, ISPEP, knows it has a 42% market share in one region of the province. The marketing department conducts a blind taste test of 70 people at the local mall.
What is the probability that fewer than 25 people will choose ISPEP.

8. Practice Questions!
Page 449 #1, 5, 8, 10