Chapter 7, Problem 94CRE

Hand Washing Ignaz Semmelweiss (1818-1865) was the doctor who first encouraged other doctors to wash their hands with disinfectant before touching patients. Before the new procedure was established, the rate of infection at Dr. Semmelweiss’s hospital was about $10\%.$ Afterward the rate dropped to about $1\%$. Assuming the population proportion of infections was $10\%,$ find the probability that the sample proportion will be $1\%$ or less, assuming a sample size of 200. Start by checking the conditions required for the Central Limit Theorem to apply.