Question

Five state officials are listed to the right. a. List the 10 possible samples (without replacement) of size 33 that can be obtained from the population of five officials. Lieutenant GovernorLieutenant Governor (Upper LL) Secretary of StateSecretary of State (Upper SS) Attorney GeneralAttorney General (Upper AA) RepresentativeRepresentative (Upper RR) Press SecretaryPress Secretary (Upper PP) b. If a simple random sampling procedure is used to obtain a sample of threethree officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample?

292

likes1460 views

Sigrid

4.5

86 Answers

a. To find all possible samples of size 3 that can be obtained from a population of 5 officials, we can use combinations.

There are 5 officials, denoted as LL, SS, AA, RR, PP.

The number of ways to choose a sample of 3 officials without replacement from 5 officials is given by{5 \choose 3} = \frac{5!}{3!(5-3)!} = 10 .

The 10 possible samples are:

1. LL, SS, AA

2. LL, SS, RR

3. LL, SS, PP

4. LL, AA, RR

5. LL, AA, PP

6. LL, RR, PP

7. SS, AA, RR

8. SS, AA, PP

9. SS, RR, PP

10. AA, RR, PP.

b. If a sample of size 3 is chosen at random, each sample of 3 officials has the same probability of being chosen, as each sample is equally likely.

Therefore, since there are 10 total samples, the probability of choosing each sample is\frac{1}{10} .

So, the chances of the sample being the first, second, or tenth sample from the list are all\frac{1}{10} .

\textbf{Answer:} The chances that the sample is the first, second, or tenth sample are all \frac{1}{10} .

There are 5 officials, denoted as LL, SS, AA, RR, PP.

The number of ways to choose a sample of 3 officials without replacement from 5 officials is given by

The 10 possible samples are:

1. LL, SS, AA

2. LL, SS, RR

3. LL, SS, PP

4. LL, AA, RR

5. LL, AA, PP

6. LL, RR, PP

7. SS, AA, RR

8. SS, AA, PP

9. SS, RR, PP

10. AA, RR, PP.

b. If a sample of size 3 is chosen at random, each sample of 3 officials has the same probability of being chosen, as each sample is equally likely.

Therefore, since there are 10 total samples, the probability of choosing each sample is

So, the chances of the sample being the first, second, or tenth sample from the list are all

Frequently asked questions (FAQs)

What is the derivative of f(x) = sin(3x) + cos(2x) with respect to x?

+

What is the relationship between the measures of corresponding angles of two congruent triangles?

+

Find the maximum value of the function f(x) = x^3 - 6x^2 + 9x - 2 on the interval [0, 4].

+

New questions in Mathematics