Question

Suppose your statistics instructor gave six examinations during the semester. You received the following exam scores (percent correct): 92, 70, 84, 87, 90, and 75. To compute your final course grade, the instructor decided to randomly select two exam scores, compute their mean, and use this score to determine your final course grade.

1. Compute the population mean. This is your average grade based on all of your grades. (Round your answer to 2 decimal places.)

2. Compute the population standard deviation. (Round your answer to 2 decimal places.)

3. How many difference scores could be calculated if your instructor decided to random sample two of your exam scores?

4. List all possible samples of size 2 and compute the mean of each. (Round your answers to 1 decimal place.)

5. Compute the mean of the sample means and the standard error of the sample means. (Round your answers to 2 decimal places.)

6. Applying the central limit theorem, if the instructor randomly samples two of your exam scores to compute an average as your final course grade, what is the probability your final course grade will be less than 83.00? What is the probability that your final course grade will be more than 83.00? (Round your answers to 1 decimal places.)

Answer 1

(a-b)

Following table shows the calculations for populaiton mean and population standard deviation:

(c)

Since we need different samples and sampling is done without replacement so combination will be used. Number of possible different samples are

C(6,2) =15

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(d)

Following table shows all the samples and corresponding means:

	Values
Samples	value 1	value 2	sum	Mean
1	92	70	162	81
2	92	84	176	88
3	92	87	179	89.5
4	92	90	182	91
5	92	75	167	83.5
6	70	84	154	77
7	70	87	157	78.5
8	70	90	160	80
9	70	75	145	72.5
10	84	87	171	85.5
11	84	90	174	87
12	84	75	159	79.5
13	87	90	177	88.5
14	87	75	162	81
15	90	75	165	82.5
Total				1245

The mean of sample means is:

The standard error of sample means is:

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(f)

The z-score for is

The probability your final course grade will be less than 83 is

The probability your final course grade will be more than 83.33 is