Thread: Probability of biochemical experiment, distribution

In a biochemical experiment, n organisms are placed in a nutrient medium, and the number of organisms X which survive for a given period is recorded. The probability distribution of X is assumed to be given by



and otherwise

1) Calculate the probability that at most a proportion of the organisms survive, and deduce that for large n this is approximately

2) Find the smallest value of for which the probability of there being at least one survivor among the n organisms is at least 0.95

Originally Posted by acevipa

In a biochemical experiment, n organisms are placed in a nutrient medium, and the number of organisms X which survive for a given period is recorded. The probability distribution of X is assumed to be given by



and otherwise

1) Calculate the probability that at most a proportion of the organisms survive, and deduce that for large n this is approximately

2) Find the smallest value of for which the probability of there being at least one survivor among the n organisms is at least 0.95

1) Probability that at most a proportion survives is the same as the probability than at most the number that survive is survive

This is:



and the rest is just algebra.

CB