In an experiment, the target bacteria can only live in the solution with 0.7-0.9ml/l nacl. your solution has mean 0.8ml/l but standard deviation 0.05ml/l nacl. what is a lower bound of the probability that the bacteria will survive?

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%

indicate valleys, hills, steepness and gentleness of slopes.

explanation:

contour lines on a map indicate elevation, or depth. numeric notations on contour lines refer to the level of elevation, or height about sea level.

in scientific notation, the value of the  speed of light in a vacuum

  will be written as 2.995 * 10^8. when this value is represented in the form of

  a * 10^b, then, a = 2.995 and b = 8.

the value of the speed of light in a vacuum given above can also be rounded up to approximately 300000000. in this case, the scientific notation will be written as 3 *10^8.