# Sampling distributions

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##### Intros
###### Lessons
1. What is sampling?
##### Examples
###### Lessons
1. Understanding Proportions and Sample Size
There are 7 supercars competing on a racetrack. The cars are labelled {1, 2, 3, 4, 5, 6, 7}.
Find,
1. The proportion of odd numbered cars
2. How many different samples are there if we chose samples of 3 cars
i. With replacement?
ii. Without replacement?
2. Connecting Sample Proportions to Population Proportions
Alice, Bob, Cole, Daisy, and Eve are all the students in a 10th grade class. Alice, Cole and Eve brought a lunch to class while the rest of the class did not.
1. Find the proportion of students who brought a lunch to class.
2. Make a list of all samples of students of size 2
3. Find the probability of each sample occurring.
4. What is the sample proportion of each sample?
5. Find the average of all the sample proportions and explain the significance of your findings.
3. Connecting Sample Means to the Population Mean
Uncle Sammy grows prize winning big zucchinis. The weights of his four largest zucchinis are given in the table below:
 Zucchini: A B C D Weight: 7 lbs 9 lbs 11 lbs 5 lbs
1. What is the average weight of all the zucchinis Uncle Sammy grows?
2. Make a list of all samples of size 2 for the zucchinis Uncle Sammy grows.
3. What is the probability that each sample gets picked?
4. What is the average weight of each sample?
5. Find the average weight of all the sample means.