Exploring The Central Limit Theorem and Sample Proportions in Fathom
Find the true proportion of 4 year old pennies from the population of pennies
p=
This value is called a parameter
since is describes the population
Use samples of size n = 10 to plot part of the sampling distribution for
samples of size n = 10. In each sample, calculate the proportion of 4 year old
pennies. Use 1000 samples of size n = 10.
1.) Paste your graph below. Also paste the summary table below.
2.) Theoretical mean and standard deviation for sampling distributions of
sample proportions:
 pˆ  p
 pˆ 

p(1 p)
n
3.) What is the probability that a random sample of 10 pennies will contain
p  .03 )
less than 3% of 4 year old pennies in the sample? P( µ
Conditions for normality :
np  10
n(1-p)  10
Use samples of size n = 100 to plot part of the sampling distribution for
samples of size n = 100. In each sample, calculate the proportion of 4 year
old pennies. Use 1000 samples of size n = 100.
1.) Paste your graph below. Also paste the summary table below.
2.) Theoretical mean and standard deviation for sampling distributions of
sample proportions:
 pˆ  p
 pˆ 

p(1 p)
n
3.) What is the probability that a random sample of 100 pennies will contain
p  .03 )
less than 3% of 4 year old pennies in the sample? P( µ
Conditions for normality :
np  10
n(1-p)  10
Use samples of size n = 200 to plot part of the sampling distribution for
samples of size n = 200. In each sample, calculate the proportion of 4 year
old pennies. Use 1000 samples of size n = 200.
1.) Paste your graph below. Also paste the summary table below.
2.) Theoretical mean and standard deviation for sampling distributions of
sample proportions:
 pˆ  p
 pˆ 

p(1 p)
n
3.) What is the probability that a random sample of 200 pennies will contain
p  .03 )
less than 3% of 4 year old pennies in the sample? P( µ
Conditions for normality :
np  10
n(1-p)  10

(.053)(1  .053) 
p : N  .053,
Assumptions met therefore µ

200

