# Example code for finding (standard) normal probabilities in R

# The command pnorm computes normal probabilities 

# It computes the probability that a standard normal r.v. is less than (or equal to) 
# a certain value.  So R gives us P(Z < value), whereas Table II in the book gives 
# us P(0 < Z < value) 

# Suppose our random variable Z is standard normal 

# Let's answer the following questions which were given in class 

# 1. What is the probability Z is between 0 and 1.24? 
pnorm(1.24) - pnorm(0)

# 2. What is the probability Z is greater than 1.24?  
1 - pnorm(1.24)

# 3. What is the probability Z is less than 1.24?  
pnorm(1.24)

# 4. What is the probability Z is between -0.54 and 0? 
pnorm(0) - pnorm(-0.54)

# 5. What is the probability Z is less than -0.54? 
pnorm(-0.54)

# 6. What is the probability Z is between -1.75 and -0.79? 
pnorm(-0.79) - pnorm(-1.75)

# 7. What is the probability Z is between -0.79 and 1.16? 
pnorm(1.16) - pnorm(-0.79)

#  What if X is normal with mean 266 and standard deviation 16 (like the pregnancy 
# example in class)?  If you're clever, you can let R standardize for you, 
# as the eighth example here will show: 

# 8. What is the probability X is between 260 and 280? 
pnorm((280-266)/16) - pnorm((260-266)/16)

# or alternatively:
pnorm(280,mean=266,sd=16) - pnorm(260,mean=266,sd=16)

# Compare to the results we got in class using the tables 

# The difference is:  R can do these for any values of Z