Question

The mean dying rate of mice administered to a given dosage of an experimental drug is 45with a variance of 25. What is the probability that among the mice, which received the drug, more than 50 will die? Assume normality

Answer 1

Let $X=$ the number of mice that died: $X\sim N(\mu, \sigma^2).$

Given $\mu=45, \sigma^2=25.$

$$P(X>50)=1-P(X\leq 50)$$

$$=1-P(Z\leq \dfrac{50-45}{\sqrt{25}})=1-P(Z\leq 1)$$

$$\approx0.158655$$