Answer:
a) 15 to 35 approximately 95%
(b) 10 to 40 approximately almost all
(c) 20 to 30 approximately 68%
Explanation:
The data have a bell-shaped distribution which means the data is equally distributed on both sides of the mean.
We have the mean at 25 and a standard deviation of 5 which means that the interval is for each of the values of 5 .
The mean would be u and
The first value would be u ±σ = 25 ± 5= 20 and 30 (68 % )
The second value will be u ± 2σ= 25± 10 = 15 and 35 (95%)
The third value will be u ± 3σ= 25 ± 15 = 10 and 40 (99.7 % almost all)
In the figure below the light blue region gives u ±σ on both sides of the mean
, dark blue gives u ± 2σ values on both sides of the mean and grey gives
u ± 3 σ values on both sides of the mean.
It is obvious that 68 % of the data is contained in the u ±σ light blue region, 95 % of the data in the u ± 2σ dark blue including light blue and 99.7 % in the u ± 3σ all colored regions.
