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(Please use the following directions to answer all the questions 1-14:) Directions: Answer the following questions and solve the following problems about a sampling distribution for the parametric value, median.

Consider the number of students, x, from each of the five eighth grade classes at Majestic Mountain Elementary School who will be participating in a field trip to the fish hatchery:

X 20 21 22 24 25

Construct the probability distribution,, of the sampling distribution of the medians,, of all possible samples of size three.

[COMMENTS & HINTS: The sample median can be symbolized as x and eads as x-tilde. How many samples of size three are possible from a population of size five? Does order matter in selecting these samples? No. List all the possible samples in order to find their medians, P(x). Then, create a table that lists the chance of each of the median being randomly selected.]

Question 1)

Compute the median of this small population. ????

Question 2)

How many samples of size three can be collected from this small population of five????

Question 3)

Construct each of the samples carefully.

[HINTS & COMMENTS: Be systematic, listing the items numerically in each sample of size three, starting with the smallest population member, to assure all possible sample are created. Does order matter? No. The total number of samples should be a small two-digit number.]

Compute the sample medians for each sample.

How many times does the value 20 occur as a sample median??????

Question 4)

Again considering the sample medians for each sample, how many times does the value 21 occur as a sample median?????

Question 5)

Again considering the sample medians for each sample, how many times does the value 22 occur as a sample median????

Question 6)

Again considering the sample medians for each sample, how many times does the value 24 occur as a sample median????

Question 7)

Again considering the sample medians for each sample, how many times does the value 25 occur as a sample median????

Question 8)

If a sample is selected at random, what is the probability that its sample median is 20?????

[HINTS & COMMENTS: Recall the total number of samples. Express the answer as a whole percentage with percent symbol.]

Question 9)

If a sample is selected at random, what is the likelihood that its sample median is 21 ???? [HINTS & COMMENTS: Recall the total number of samples. Express the answer as a whole percentage with percent symbol.]

Question 10)

If a sample is selected at random, what is the likelihood that its sample median is 22 ??? [HINTS & COMMENTS: Recall the total number of samples. Express the answer as a whole percentage with percent symbol.]

Question 11)

If a sample is selected at random, what is the likelihood that its sample median is 24 ??? [HINTS & COMMENTS: Recall the total number of samples. Express the answer as a whole percentage with percent symbol.]

Question 12)

If a sample is selected at random, what is the likelihood that its sample median is 25???

[HINTS & COMMENTS: Recall the total number of samples. Express the answer as a whole percentage with percent symbol.]

Question 13)

What is the apporpriate and necessary sum of the five previously reported probabilities, since they represent all possible outcomes of sample medians for samples of size three taken from this small populationof size five? ??? {HINT: Express as a whole percentage with percent symbol.]

Question 14)

Using the previous six answers, complete the following probability table for the sampling distribution of the median. Express all probabilities as whole percentages with percent symbols.!!!

Sample Median, x	Probability, P(X)
20	??
21	??
22	??
24	??
25	??
total probability	??