Question

1. Assume that systolic blood pressure for adult women is normally distributed with a mean of 125.17 with a variance of 107.0. An individual woman is selected from the population. Find the following probabilities.
   1. 1. What is the probability that her systolic blood pressure is less than 125.17
   2. 2. What is the probability that her systolic blood pressure is between 112 and 140?
   3. 3. What is the probability that her systolic blood pressure will be greater than 140?

please use R and show me the code that you used? My main issue is that since not all of these are whole numbers I am a bit confused on how to plug this into R. Thanks!!

Answer 1

We will use the code pnorm in R as:

pnorm(q, mean, sd)
example:

pnorm(1.96, 0, 1)
Gives the area under the standard normal curve to the left of 1.96,i.e. ~0.975

R code

#Probability that her systolic blood pressure is less than 125.17
pnorm(125.17,mean=125.17,sd=107^0.5)
#Probability that her systolic blood pressure is between 112 and 140
pnorm(140,mean=125.17,sd=107^0.5)-pnorm(112,mean=125.17,sd=107^0.5)
#Probability that her systolic blood pressure is greater than 140
1-pnorm(140,mean=125.17,sd=107^0.5)

R code with output.

> #Probability that her systolic blood pressure is less than 125.17
> pnorm(125.17,mean=125.17,sd=107^0.5)
[1] 0.5
> #Probability that her systolic blood pressure is between 112 and 140
> pnorm(140,mean=125.17,sd=107^0.5)-pnorm(112,mean=125.17,sd=107^0.5)
[1] 0.8226918
> #Probability that her systolic blood pressure is greater than 140
> 1-pnorm(140,mean=125.17,sd=107^0.5)
[1] 0.0758332