1. Day 12 AGENDA:
DG minutes
Work time --- use this time to work on practice problems from previous lessons

2. Accel Precalc
Unit #1: Data Analysis
Lesson #10: Calculating Mean, Variance, and Standard Deviation for a Binomial Distribution
EQ: How do you calculate mean, variance, and standard deviation of a binomial distribution? How are these used to interpret the data?

3. Work smarter, not harder!!
Create a probability distribution
where the random variable of
interest is number of heads
occurring when tossing 4 coins.
Recall:
X = number of heads when tossing 4 coins
HINT: You can, but you don’t have to create a sample space to complete this task.
Work smarter, not harder!!
How could you use Lists and binomialpdf to find
each value of P(xi) ?

4. (4)(0.5) = 2 (n)(p) E(X) = __________________________
Find the expected value for this task.
0(0.0625) + 1(0.25) +2(0.375)+3(0.25) +4(0.0625)
= 2
E(X) = __________________________
Now calculate (n)(p) ______________
(4)(0.5) = 2
WOW!!
**Formula: Mean of a Binomial Distribution
(n)(p)
µ = __________________

5. (n)(p)(q) Find the variance for this task.
(0 – 2)2(0.0625) + (1 – 2)2(0.25) + (2 – 2)2(0.375) + (3 – 2)2(0.25) + (4 – 2)2(0.0625) = 1
σ2 = ____________________________
(4)(.5)(.5) = 1
Now calculate (n)(p)(q) ______________
WOW!!
**Formula: Variance of a Binomial Distribution
(n)(p)(q)
σ2 = ____________________________

6. a Binomial Distribution
Find the standard deviation for this task.
σ = _____________________
**Formula: Standard Deviation of
a Binomial Distribution
σ = _____________________

7. X = # of twos occurring on 480 rolls of a die
Ex 1. A die is rolled 480 times. Find the mean, variance, and standard deviation of the number of 2’s that will be rolled.
X = # of twos occurring on 480 rolls of a die
Would this be a BINOMIAL DISTRIBUTION or a NORMAL DISTRIBUTION?
WHY?
I DO NOT want to create a probability distribution for this!! WHY?
(n)(p) = (480)(1/6) = 80
µ = __________________
σ2 = ________________
σ = _____________________
(n)(p)(q) = (480)(1/6)(5/6) = 66.67

8. Would this be a BINOMIAL DISTRIBUTION or a NORMAL DISTRIBUTION?
Ex 2. The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would result in twins.
Would this be a BINOMIAL DISTRIBUTION or a NORMAL DISTRIBUTION?
WHY?
X = # of twin births occurring 8000 births
µ = __________________
σ2 = ________________
σ = _____________________
(n)(p) = (8000)(0.02) = 160
(n)(p)(q) = (8000)(0.02)(0.98) = 156.8

9. Get out a sheet of paper to use for Ex 3.
Answer #6 & #7 first.

10. Now finish #1 - #5 on your own.
6. Criteria needed to be Binomial Distribution:
a. Fixed # of trials n = 10 restaurants
b. Success --- unsatisfactory Failure --- satisfactory
c. Condition of one restaurant independent of others
p = 3/7 remains the same from restaurant to
restaurant
Yes, this scenario meets the criteria for a binomial distribution.
7. NO, binomial distribution simply means there are only two outcomes, NOT the probabilities are 50% and 50%.
Now finish #1 - #5 on your own.

11. Only because it’s a Binomial Distribution

12. Assignment:
Practice Worksheet: Calculating Mean, Variance, and Standard Deviation of Binomial Distributions