Answer:
Interval ( 24 ; 40 ) has 136 participants
Interval ( 16 ; 40 ) has 163 participants
Step-by-step explanation:
Normal distribution.
As variance is 64 then standard deviation is σ = 8
And mean μ₀ = 32
We can see that μ₀ ± σ is 32 ± 8
The interval ( 32- 8 ; 32+8 ) is ( 24 ; 40 )
By empirical Rule we know that μ₀ ± σ contains 68% of the population then 200*0,68 = 136
The number of participants between 24 and 40 is 136
By symmetry of these 136 half of them are between 32 and 40 ( 136/2 = 68 ) ( between mean and 40 )
Now in the interval ( 16 ; 40 ) we note that 16 is 32 - 16 = 16 or μ₀ - 2σ
And again by empirical rule μ₀ ± 2σ has 95 % of the population that means 200*0.95 = 190 and by symmetry 190/2 95 are between μ₀ - 2σ, therefore
95 people are between μ₀ - 2σ or between ( 16 ; 32 ) and between ( 32 ; 40 ) there are 68 people then
The interval ( 16 ; 40 ) has 95 + 68 = 163 participants
