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