Answer:
a) σ = 0,1612
b) P [ 11,75 < X < 12,35] = 0,92,44 or 92,44 %
Step-by-step explanation:
NOTE: I assume the unusable length s 11,5 and less
a) For a normal distribution, the probability of P = 0,01 corresponds to z(score) = -3,1 then:
- 3,1 = ( X - μ₀ ) / σ
- 3,1 = (11,5 - 12 )/ σ
-3,1 = - 0,5 / σ
σ = 0,1612
b) If σ = 0,1612
P [ 11,75 < X < 12,35]
z₁ (score) = ( 11,75 - 12 ) / 0,1612
z₁ = - 0,25/ 0,1612
z₁ = -1,55
From z table P [ 11,75 < X] = 0,0606
z₂ (score) = ( 12,35 - 12) / 0,1612
z₂ = 0,35 / 01612
z₂ = 2,17
From z table P [ X < 12,35] = 0,9850
Finally P [ 11,75 < X < 12,35] = 0,9850 - 0,0606
P [ 11,75 < X < 12,35] = 0,92,44 or 92,44 %
