Question

Typhoid fever is more common in developing countries with poor sanitation and greater incidence of food contamination. The mean duration of this illness is approximate 4 weeks. Periodically, a team of doctors randomly selects 11 patients with typhoid fever and carefully measures the duration of the illness. If the mean duration is greate than 4.5 weeks, then a health alert is issued. Suppose the duration of this illness is normally distributed with standard deviation one week. (Round your answers to four decimal places.) (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 4.4 weeks. What is the probability that a health alert will be issued?

Answer 1

Given data, mean(4) = 4 weeks Std deu Co)= l weed Sample size cm=11. Std erioe of sample means 20.3015 @ requiered probability is PCac4.5). Plac 4.5) - P(xsdt < 9:30) 4.5-4) 0.3015) - P( 14 6 56) . = 1019499] (from z-table) 10 probability of health alert assured can be written as - P(x>4.5)= 1-0-9495 10.0501 © of mean= 4:4 weeks PC heath alert issued & P(x745) 4-5-4-4) -PC2> 7.8015) =PC2>0.3316) F-PC220-3310 El-0.6285 Crong Zrtibles 559-3715)