# Import the babies data (in the import dataset box, we changed the delimiter from "comma" to "whitespace")
library(readr)
babies <- read_table2("babies.csv")

# Plot the histogram of the mothers' ages (and notice one or two are apparently 99 years old...)
# Really 99 is used to indicate the mother's age is unknown
hist(babies$age, xlab = "Mothers' age")

# To relace 99 with the median mothers' age:
# Compute the median age and store it in the variable median_age
median_age <- median(babies$age)

# Replace any values of 99 in the age column with the median age.
babies$age[babies$age == 99] <- median_age

# Plot the age histogram one more time to check it looks more realistic
hist(babies$age)

# compute P(X <= 3) where X~N(2,5^2).  
# That is, where X has a normal distribution with mean 2 and variance 5^2.
pnorm(q = 3, mean = 2, sd = 5)

# compute P(X > 3) where X~N(2,5^2)
1 - pnorm(q = 3, mean = 2, sd = 5)

# compute P(1 < X < 4) by computing P(X < 4) - P(X < 1), where X~N(2,5^2)
pnorm(q = 4, mean = 2, sd= 5) - pnorm(q =1, mean =2, sd = 5)

# try to approximate the blood pressure range in the example problem
a = 7
pnorm(q = 120 + a, mean = 120, sd= 8) - pnorm(q = 120 -a, mean =120, sd =8)
a = 6.9
pnorm(q = 120 + a, mean = 120, sd= 8) - pnorm(q = 120 -a, mean =120, sd =8)
a = 6.5
pnorm(q = 120 + a, mean = 120, sd= 8) - pnorm(q = 120 -a, mean =120, sd =8)
a = 6.7
pnorm(q = 120 + a, mean = 120, sd= 8) - pnorm(q = 120 -a, mean =120, sd =8)