Question

Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?

68% of the data points lie between 10 and 14.




68% of the data points lie between 8 and 12.




68% of the data points lie between 10 and 18.




68% of the data points lie between 10 and 16.

Answer 1

----σ-------σ-------μ------σ------σ--------
-2σ -1σ 14 +1σ +2σ
-6 -10 14 +18 +22

68% of the data points lie between 10 and 18.

Answer 2

Answer with explanation:

Standard Deviation of Data Set = 4

Mean of Data Set = 14

Normal Distribution curve is a bell Shaped curve ,described by mean and Standard Deviation.It is Symmetrical on both sides of mean, and Spread between two points is determined by Standard Deviation.

Option D:

68% of the data points lie between 10 and 18.

Points on left of mean =14-4=10,6,2

point on right of mean = 14 +4=18,22,26

That is , we can say that 68% of the data lie within 1 Standard Deviation.