Question

select the correct answer. which data set is the farthest from a normal distribution? a. 2,3,3,4,4,4,5,5,6 b. 3,4,5,6,6,7,7,7,8,8,9,10 c. 0.9,1.0,1.0,1.1,1.1,1.1,1.2,1.2,1.3 d. 4,4,4,5,5,6,7,7,8,8,8 e. 2,4,5,5,6,6,7,7,7,8,8,9,9,10

Explanation:

Step1: Recall normal - distribution properties

A normal distribution is symmetric about the mean. We can check the symmetry of each data - set.

Step2: Analyze Option A

The data set A: 2, 3, 3, 4, 4, 4, 5, 5, 6. The middle value is 4, and it is somewhat symmetric around 4.

Step3: Analyze Option B

The data set B: 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10. It is relatively symmetric around 7.

Step4: Analyze Option C

The data set C: 0.9, 1.0, 1.0, 1.1, 1.1, 1.1, 1.2, 1.2, 1.3. It is symmetric around 1.1.

Step5: Analyze Option D

The data set D: 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8. It is somewhat symmetric around 6.

Step6: Analyze Option E

The data set E: 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10. The lower - end values (2, 4) are more spread out from the middle values compared to the upper - end values, and it is the least symmetric among all the data sets.

Answer:

E. 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10