Question

ne average age of doctors in a certain hospital is 43,0 years old. Suppose the distribution of ages s normal and has a standard deviation of 8.0 years. If 25 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 43.8 years. Assume that the variable is normally distributed [6 marks) 14. A mandatory competency test for high school students has a normal distribution with a mean of 400 and a standard deviation of 100, The top 3% of students receive $500, what is the minimum score you would need to receive this award? 17 marks]

Answer 1

Note that sample mean X follows a Normal distribution with Mean μ = 43 Standard deviation σ/Vn 1.6 Note that z- (X-H)/(0/n) (x-43)/1.6 -(Eq.1) follows standard Normal. When 43.8, from (Eq.1), z 0.5 P(X<43.8)-P(Zk0.5)-0.6915 if using Normal table) Given that X follows a Normal distribution with Mean -u 400 Note that (x-μ)/σ (x-400)/100 follows standard Normal. z: We need to find x such that P(X>x) 0.03 P(Xx) 1-0.03 0.97 → P(Z < ((x. 400)/ 100))]= 0.97 (x-400)/100 1.88 (Normal table) x- 588 (ans)