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

Answer:

A) No

B) No

C) Yes

Step-by-step 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