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HW6_PARTI_Solutions

HW6_PARTI_Solutions - STA 368 HW 6 Solutions(Part 1 Fall...

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STA 368 HW 6 Solutions (Part 1) Fall 2009 Part 1: Simulation of the binomial and normal distributions Question 1: Given a normal distribution with mean 30 and standard deviation 6, Use R to find (a) the normal curve area to the right of x=17. R code: -------------------------------------- x<-17 mu<- 30 std<- 6 1-pnorm(x, mu, std) -------------------------------------- R output: -------------------------------------- [1] 0.9848699 -------------------------------------- (b) the normal curve area between x=32 and x=41. R code: -------------------------------------- x1<-32 x2<-41 mu<- 30 std<- 6 pnorm(x2, mu, std)-pnorm(x1,mu,std) -------------------------------------- R output: -------------------------------------- [1] 0.3360648 -------------------------------------- (c) The value of x that has 80% of the normal-curve area to the left;
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STA 368 HW 6 Solutions (Part 1) Fall 2009 R code: -------------------------------------- percent<-0.8 mu<- 30 std<- 6 qnorm(percent, mu, std) -------------------------------------- R output: -------------------------------------- [1] 35.04973 -------------------------------------- (d) The two values of x that contain the middle 75% of the normal-curve area. R code: -------------------------------------- p.upper<-1-(1-0.75)/2 p.lower<-(1-0.75)/2 mu<- 30 std<- 6 qnorm(p.upper, mu, std) qnorm(p.lower,mu,std) -------------------------------------- R output: -------------------------------------- > qnorm(p.upper, mu, std) [1] 36.90210
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