Question: Public Health and Nutrition Typhoid fever is more common in developing countries with poor sanitation and greater incidence of food contamination. The mean duration of this illness is approximately 4 weeks.14 Periodically, a team of doctors randomly selects 10 patients with typhoid fever and carefully measures the duration of the illness. If the mean duration is greater than 4.5 weeks, then a health alert is issued. Suppose the duration of this illness is normally distributed with standard deviation one week.
a. Find the probability that the sample mean duration is less than 4.5 weeks.
b. Find the probability that a health alert is issued.
c. Suppose the true mean duration has increased to 4.3 weeks. What is the probability that a health alert will be issued?