In adults, the pneumococcus bacterium causes 70% of pneumonia cases. In a random sample of 84 adults who have pnuemonia, let Y = the number of whose pneumonia was caused by the pneumococcus bacterium. Use the Central Limit Theorem to approximate P(Y Solution Given n=84, p=0.7 mean=n*p=84*0.7=58.8 standard deviation=n*p*(1-p)=sqrt(84*0.7*0.3)= 4.2 So the probability is P(X=52)= P(51.5.