R Notebook

manually:

#the bottom of the graph. the minimum and maximum numbers you are dealing with.
x <- seq(from = 70, to = 130)

#the normal distribution for the minimum and maximum values with an average of 100, and a standard deviation of 10.
y <- dnorm(x, mean = 100, sd = 10)

#plot the distribution with a line type graph and make the line color red.
plot(x,y, type = "l", col = "red", main = "test graphic")

#set up to color the relevant area under the curve.
#Specify the area between 70 and 90.
x2 <- seq(70,90)

#the top part. specify the part of the normal distribution line we want to shade under.
y2 <- dnorm(x2, mean = 100, sd = 10)

#shade the area of 70 to 90 including everything in between, and the area below the normal distribution line.
polygon(x = c(70,x2,90), y = c(0,y2,0), col = "red")

abline(v = 81, col = "green", lwd = 5)

p_value <- pnorm(90, mean = 100, sd = 10)
p_value

[1] 0.1586553