Answer:
The probability of survival is at least 75%
Explanation:
Since we do not know the probability distribution of the concentration of the solution, we can not determine the exact probability of survival. Nevertheless, we can use the Chebyshev inequality, that applies to any probability distribution, to calculate the lower bound.
It states that
P( | X - µ | ≤ kσ ) ≥ 1- 1/k²
this means that the probability that X is not further than k standard deviations from the mean (µ) is at least 1- 1/k² , where k >1
in our case,
k1= (X1 - µ) / σ = (0,9 - 0,8 ) / 0,05 = 2
k2=(X2 - µ) / σ = (0,7- 0,8 ) / 0,05 = -2
therefore k=k1=k2=2 and
P( | X - µ | ≤ 2σ ) ≥ 1- 1/2²= 3/4=75%
consequently, the lower bound of the probability of survival is 75%
