Problem set 1
Assume body heights (inches) for the population of 8-year old boys are X ∼ N(μX = 51,σX = 3). If we choose a boy at random, then what is the probability that his height exceeds 50 inches?
1-pnorm((50-51)/3)
## [1] 0.6305587
There will be a 63% chance of randomly choosing a boy with a height exceeding 50 inches.
Problem set 2
Assume body heights (inches) for the population of 8-year old boys are X ∼ N (μX = 51, σX = 3), and heights (inches) for the population of 8-year old girls are Y ∼ N(μY = 53, σY = 2.5). If we choose a boy and a girl at random, then what is the probability that the boy is taller than the girl?
X = 1-pnorm((50-51)/3)
Y = 1-pnorm((50-53)/2.5)
pnorm(X > Y)
## [1] 0.5
There will be a 50% chance that the boy will be taller than the girl if we choose a boy and girl at random.