Download Calculating Mean, Variance, and Standard Deviation for a Binomial

Accel Math III
Unit #1: Data Analysis
Lesson #7: Calculating Mean, Variance, and
Standard Deviation for a Binomial
Distribution
EQ: How do you calculate mean, variance, and
standard deviation of a binomial distribution
and how are these used to interpret the data?
Recall:
Create a probability distribution where the
random variable of interest is number of heads
occurring when tossing 4 coins.
[HINT: You can, but you don’t have to create a sample
space to complete this task.]
X
P(X)
Find the expected value for this task.
E(X) = __________________________
Now calculate (n)(p)
Formula:
______________
Mean of a Binomial Distribution
µ = __________________
Find the variance for this task.
σ2
= ____________________________
Now calculate (n)(p)(q) ______________
Formula:
σ2
Variance of a Binomial Distribution
= ____________________________
Find the standard deviation for this task.
σ = _____________________
Now calculate
(n)( p)(q) _____________
Formula: Standard Deviation of a Binomial Distribution
σ = _____________________
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.
µ = __________________
σ2
= ________________
σ = _____________________
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.
µ = __________________
σ2
= ________________
σ = _____________________
Ex 3.
Assignment:
Practice Worksheet: Calculating Mean,
Variance, and Standard Deviation of Binomial
Distributions
Test #1 Unit 1