Answer:
Porcentage of students score below 62 is close to 0,08%
Step-by-step explanation:
The rule
68-95-99.7
establishes:
The intervals:
[ μ₀ - 0,5σ , μ₀ + 0,5σ] contains 68.3 % of all the values of the population
[ μ₀ - σ , μ₀ + σ] contains 95.4 % of all the values of the population
[ μ₀ - 1,5σ , μ₀ + 1,5σ] contains 99.7 % of all the values of the population
In our case such intervals become
[ μ₀ - 0,5σ , μ₀ + 0,5σ] ⇒ [ 78 - (0,5)*8 , 78 + (0,5)*8 ] ⇒[ 74 , 82]
[ μ₀ - σ , μ₀ + σ] ⇒ [ 78 - 8 , 78 +8 ] ⇒ [ 70 , 86 ]
[ μ₀ - 1,5σ , μ₀ + 1,5 σ] ⇒ [ 78 - 12 , 78 + 12 ] ⇒ [ 66 , 90 ]
Therefore the last interval
[ μ₀ - 1,5σ , μ₀ + 1,5 σ] ⇒ [ 66 , 90 ]
has as lower limit 66 and contains 99.7 % of population, according to that the porcentage of students score below 62 is very small, minor than 0,15 %
100 - 99,7 = 0,3 %
Only 0,3 % of population is out of μ₀ ± 1,5 σ, and by symmetry 0,3 /2 = 0,15 % is below the lower limit, 62 is even far from 66 so we can estimate, that the porcentage of students score below 62 is under 0,08 %
r^2