a. Using R language
x <- rnorm(1000, mean = 70,sd = 3.5)
y <- rnorm(1000, mean = 66,sd = 3)
hx1 <- density(x)
hx2 <- density(y)
plot(hx1,col="red", ylim = c(0,0.15), main = "")
lines(hx2, col="green")
b.
P(x<K) = pnorm(k, mean, sd)
P(x>=68) = 1 - pnorm(68, 70, 3.5)
= 0.7161454
c.
P(x<K) = pnorm(k, mean, sd)
P(x>=68) = 1 - pnorm(68, 66, 3)
= 0.2524925
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