Solve my High school statistics question. Here is a photo

Marian Sanforonio

Answered question

2022-05-30

Answer & Explanation

Don Sumner

Skilled2023-05-18Added 184 answers

To determine the number of different samples of size

n

that can be drawn from a population of size

N

, we use the formula for combinations, which is denoted as

(\binom{N}{n})

.
For the first case (number 23), we have a population size of

N = 8

and we want to draw samples of size

n = 4

. The number of possible samples can be calculated as:

(\binom{8}{4}) = \frac{8!}{4! (8 - 4)!} = \frac{8!}{4! 4!}

Simplifying further:

(\binom{8}{4}) = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4! 4 \times 3 \times 2 \times 1}

The

4!

terms cancel out:

(\binom{8}{4}) = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}

Evaluating this expression:

(\binom{8}{4}) = \frac{1680}{24} = 70

Therefore, the number of possible samples of size 4 that can be drawn from a population of size 8 is 70.
For the second case (number 24), we have a population size of

N = 10

and we want to draw samples of size

n = 2

. Using the same formula:

(\binom{10}{2}) = \frac{10!}{2! (10 - 2)!} = \frac{10!}{2! 8!}

Simplifying:

(\binom{10}{2}) = \frac{10 \times 9 \times 8!}{2! 8!}

The

8!

terms cancel out:

(\binom{10}{2}) = \frac{10 \times 9}{2!}

Evaluating this expression:

(\binom{10}{2}) = \frac{90}{2} = 45

Therefore, the number of possible samples of size 2 that can be drawn from a population of size 10 is 45.

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