# topic 11 d part 2 more on the normal distribution

source( "../gnrnd4.R")
gnrnd4( 1774459804, 12500743)
head(L1)
tail(L1)
mu <- mean(L1)
mu
source("../pop_sd.R")
sigma <- pop_sd( L1 )
sigma
     # Create L2 by subtracting mu from L1
L2 <- L1 - mu
mean( L2 )
pop_sd(L2)
     # Create L3 by dividing L2 by sigma
L3 <- L2 / sigma
mean( L3 )
pop_sd( L3 )

     #  for a special population find P( X < 88 )
z <- ( 88 - mu ) / sigma
z
pnorm( z )
     # problem 1
z <- (12 -18.4) / 4.6
z
pnorm( z )
     # problem 2
z <- (5 - -9.7) / 6.1
z
pnorm( z, lower.tail=FALSE )
     # problem 3
z_high <- (145-134) / 15
z_low <- (120 - 134) /15
z_high
z_low
pnorm( z_high ) - pnorm( z_low )
     # problem 4
z <- qnorm(0.23)
z
y <- z*17 + 244
y
     # problem 5
z <- qnorm(0.05, lower.tail=FALSE)
z
y <- z*5.8 + 47.2
y
     # redo problem 1
pnorm( 12, mean=18.4, sd=4.6)
     # redo problem 2
pnorm( 5, mean=-9.7, sd=6.1, lower.tail=FALSE)
     # redo problem 3
pnorm( 145, mean=134, sd=15) -
  pnorm( 120, mean=134, sd=15 )
     # redo problem 4
qnorm( 0.23, mean=244, sd=17 )
     # redo problem 5
qnorm( 0.05, mean=47.2, sd=5.8, lower.tail=FALSE)
     #
     # For N( 500, 100 ) find the 95th percentile
qnorm( 0.95, mean=500, sd=100 )