xv = seq(140, 215, .1)
plot(xv, dnorm(xv, mean=175, sd = 8))
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l")
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l", ylim=c(0,.7))
points(xv, dnorm(xv, mean=175, sd = 8/sqrt(100)), type ="l", ylim=c(0,.7))
points(xv, dnorm(xv, mean=175, sd = 8/sqrt(1000)), type ="l", ylim=c(0,.7))
xv = seq(140, 215, .1)
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l", ylim=c(0,.7))
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l", ylim=c(0,.5))
plot(xv, dnorm(xv, mean=175, sd = 8/sqrt(2)), type ="l", ylim=c(0,.5))
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l", ylim=c(0,.5))
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l")
plot(xv, dnorm(xv, mean=175, sd = 8), type ="l", ylim=c(0,.5))
163+175
338/2
plot(xv, dnorm(xv, mean=169, sd = 8), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(2)), type ="l", ylim=c(0,.5))
abline(v = 169, lty="dashed")
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(5)), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(10)), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(20)), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(50)), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(100)), type ="l", ylim=c(0,.5))
points(xv, dnorm(xv, mean=169, sd = 8/sqrt(1000)), type ="l", ylim=c(0,.5))
15/4
1-pnorm(-2)
1.96*3.75