Question

Below are the final exam scores of 20 Introductory Statistics students.

Student	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Score	71	76	77	77	79	80	80	80	81	81	84	84	85	86	86	86	86	87	89	93

The mean exam score is 82.4 with a standard deviation of 5.14.

1. How many of the exam scores in the sample are within one standard deviation of the mean?

2. How many of the exam scores in the sample are within two standard deviations of the mean?

3. How many of the exam scores in the sample are within three standard deviations of the mean?

4. Based on the empirical rule, do these data appear to follow a normal distribution?

A. No
B. Yes

Answer 1

Answer 2

Answer 3

1:

The interval corresponding to within one standard deviation of the mean is

Out of 20 data values, 14 are in the above interval. The percentage of scores within one SD of mean is

(14 /20) * 100% = 70%

2:

The interval corresponding to "within two standard deviations of the mean" is

Out of 20 data values, 18 are in the above interval. The percentage of scores within one SD of mean is

(18 /20) * 100% = 90%

3:

The interval corresponding to "within 3 standard deviations of the mean" is

Out of 20 data values, 20 are in the above interval. The percentage of scores within one SD of mean is

(20 /20) * 100% = 100%

4:

According to empirical rule, 68% data values lies within one SD of mean, 95% data values within 2 SD of mean and 99.7% data values lies within 3 SD of mean.

So we can say that data approximately follows normal distribution.