Question

If a particular set of data is approximately normally distributed, we would find that approximately A) 2 of every 3 observations would fall between ±1 standard deviation around the mean. B) 4 of every 5 observations would fall between ±1.28 standard deviations around the mean. C) 19 of every 20 observations would fall between ±2 standard deviations around the mean. D) All of the above.

Answer 1

A) No

B) No

C) Yes

Explanation:

A) 2 out of three observations is equal to

2/3 = 0.67 or 67 %

We know tha the interval

[μ - σ/2 , μ + σ/2] is approximately 68.3 % of the values

Therefore 2 out of 3 would not fall in that interval

B)

4 out of 5 is 4/5 = 0,8 or 80 % If we examine the interval

[μ - σ , μ + σ ] which is approximately 95. Then value 4/5 ( 0,8)

Therefore 0,8 is out of the interval

C) 19/20 = 0,95 or 95 % is almost exact the value for the interval

[μ - 1.5σ , μ + 1.5σ ] That value is inside μ - 2σ , μ + 2