Sampling
Distribution
Hans Peterson
Exam 2
• Mean = 87.55%
Review: Parameters and Statistics
• Parameter: a constant that describes a
population, e.g., μ from a Normal distribution
• Statistic: a random variable calculated from a
sample e.g., x̄
• These are related but are not the same!
• For example, the average age of the UCSD
undergraduate student population µ = 20.25
(parameter), but the average age in any sample xbar (statistic) may differ from µ
Population Distributions
• How can we represent population data with sample data?
Population Distributions
• How can we represent population data with sample data?
Population Distributions
• How can we represent population data with sample data?
Population Distributions
• How can we represent population data with sample data?
Population Distributions
• How can we represent population data with sample data?
µ=
ΣX
N
SS =
2
X
µ
(
−
)
∑
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• How can we represent population data with sample data?
Sample1 [0,0,0,17,32]; x̄1 = 9.8
Sample2 [0,2,31,31,32]; x̄2 = 19.2
Sample3 [0,0,32,32,32]; x̄3 = 19.2
Sample4 [2,31,32,32,32]; x̄4 = 25.8
Sample5 [0,2,31,31,32]; x̄5 = 19.2
…etc
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2; Sample1 [0,32] x̄1 = 16
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2; Sample1 [0,32] x̄1 = 16
B. N=25; Sample1 [2,24…32] x̄1 = 17
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough. As the N of a sample goes up,
so does the rate at which it approaches a normal dist.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Population Distributions
• The central limit theorem states that the distribution of
any sample statistic will be normal or nearly normal, if the
sample size is large enough. As the N of a sample goes up,
so does the rate at which it approaches a normal dist.
A. N=2
B. N=25
µ = 17.23, σ = 11.57
Characteristics of a Sampling
Distribution
• If a population distribution has mean µ and variance σ^2, then
the sampling distribution for a statistic (for samples of size n)
has….
• Mean of the sampling distribution of the statistic equals the
population mean of that statistic, µ
• Variance of the sampling distribution of the statistic equals the
population variance divided by the sample size, σ^2/n.
• Standard Deviation of the sampling distribution of the statistic,
“standard error of the mean” (σx), equals σ/ √ n.
Sampling Distribution
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞]
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
Sample3 [X1,X2,…X∞] x̄3 = 17.23
Sample4 [X1,X2,…X∞] x̄4 = 17.23
Sample5 [X1,X2,…X∞] x̄5 = 17.23
…etc
µ = 17.23, σ = 11.57
Sampling Distribution
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
Sample3 [X1,X2,…X∞] x̄3 = 17.23
Sample4 [X1,X2,…X∞] x̄4 = 17.23
Sample5 [X1,X2,…X∞] x̄5 = 17.23
…etc
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
Sample3 [X1,X2,…X∞] x̄3 = 17.23
Sample4 [X1,X2,…X∞] x̄4 = 17.23
Sample5 [X1,X2,…X∞] x̄5 = 17.23
…etc
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √∞
x
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
Sample3 [X1,X2,…X∞] x̄3 = 17.23
Sample4 [X1,X2,…X∞] x̄4 = 17.23
Sample5 [X1,X2,…X∞] x̄5 = 17.23
…etc
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √∞
x
(σx) = 11.57/ x→∞ ≈ 0
Sample1 [X1,X2,…X∞] x̄1 = 17.23
Sample4 [X1,X2,…X∞] x̄4 = 17.23
Sample2 [X1,X2,…X∞] x̄2 = 17.23
Sample5 [X1,X2,…X∞] x̄5 = 17.23
Sample3 [X1,X2,…X∞] x̄3 = 17.23
…etc
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n
(σx) = 0
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n
(σx) = 0
x̄ = 17.39
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √25
x
(σx) = 0
x̄ = 17.39
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √25
x
(σx) = 11.57/ 5 = 2.34
(σx) = 0
x̄ = 17.39
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √25
x
(σx) = 11.57/ 5 = 2.34
(σx) = 0
x̄ = 17.39
(σx) = 2.34
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = σ/ √n = (σ ) = 11.57/ √25
x
(σx) = 11.57/ 5 = 2.34
(σx) = 0
x̄ = 17.39
(σx) = 2.34
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = 0
(σx) = σ/ √n
x̄ = 17.39
x̄ = 17.81
(σx) = 2.34
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = 0
(σx) = σ/ √n = 11.57/ √2
x̄ = 17.39
x̄ = 17.81
(σx) = 2.34
µ = 17.23, σ = 11.57
Sampling Distribution
(σx) = 0
(σx) = σ/ √n = 11.57/ √2
(σx) = 11.57/1.41 = 8.18
x̄ = 17.39
x̄ = 17.81
(σx) = 2.34
µ = 17.23, σ = 11.57
(σx) = 8.18
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1]
• Sample2 [2,2,4]
• Sample3 [1,5,5]
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1]
• Sample2 [2,2,4]
• Sample3 [1,5,5]
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1]
• Sample2 [2,2,4]
• Sample3 [1,5,5]
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1]
• Sample2 [2,2,4]
• Sample3 [1,5,5]
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4]
• Sample3 [1,5,5]
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5]
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
µ = (3.67+2.67+3) / 3 = 9.33/3
• What is your best estimate of the population mean?
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
Mean of the sampling distribution of the
statistic equals the population mean of that
statistic, µ
µ = (3.67+2.67+3) / 3 = 9.33/3
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
(σx) = σ/ √n
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
(σx) = σ/ √n
σ = √ σ^2
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
(σx) = σ/ √n
σ = √ σ^2 = √5 = 2.24
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
(σx) = σ/ √n
σ = √ σ^2 = √5 = 2.24
(σx) = 2.24 / √3
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution?
Example Problem
• The variance of some population is equal to σ^2 = 5. You
gather the following samples from the population:
• Sample1 [5,3,1] x̄1 = 3
• Sample2 [2,2,4] x̄2 = 2.67
• Sample3 [1,5,5] x̄3 = 3.67
(σx) = σ/ √n
σ = √ σ^2 = √5 = 2.24
(σx) = 2.24 / √3 = 1.29
• What is your best estimate of the population mean? µ = 3.11
• What is the standard error of the mean of the sampling
distribution? σx = 1.29
Example Problem
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
Example Problem
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
Example Problem
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
Example Problem
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
µ=2
your party?
1.3
-0.1
2.7
0.6
3.4
σ = 0.7
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
µ=2
your party?
110 pints
1.3
-0.1
_________ = 2.2 pints
50 people
2.7
0.6
3.4
σ = 0.7
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
µ=2
your party?
110 pints
1.3
-0.1
_________ = 2.2 pints
50 people
2.7
0.6
3.4
σ = 0.7
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
1.3
-0.1
0.6
2.7
3.4
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
1.3
-0.1
0.6
2.7
3.4
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n
x
1.3
-0.1
0.6
2.7
3.4
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.7
3.4
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
(σx) = .099
2.7
0.6
3.4
(σx) = .099
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
(σx) = .099
(σx) = .099
4.1
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Z = X - x̄ / σx
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Z = X - x̄ / σx
Z = 2.2 - 2 / 0.099
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Z = X - x̄ / σx
Z = 2.2 - 2 / 0.099
Z = 2.02
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Z = X - x̄ / σx
Z = 2.2 - 2 / 0.099
Z = 2.02
Example Problem
µ=2
σ = 0.7
• The average UCSD student drinks 2 pints of beer before the
Sun God Festival (with a standard deviation, σ = 0.7 pints). This
year you are planning on hosting a Sun God pre-party for 50
people, and you plan on buying a keg that contains 110 pints
of beer. What is the probability that you will run out of beer at
your party?
x̄ = 2
(σ ) = σ/ √n = .7/ √50
x
1.3
-0.1
0.6
2.099
2.7
3.4
2.198
4.1
(σx) = .099
(σx) = .099
Z = X - x̄ / σx
Z = 2.2 - 2 / 0.099
Z = 2.02