Linear Regression Model Help

#1
Hi, I don't really understand how I go about this problem. I understand regression but I need a little help here.

Question:
Reaction time to a stimulus (y seconds) is believed to be related to the amount of the drug in the bloodstream (x%) by a simple linear regression model where

E(y) = -0.1 + 0.8x
with σ = 0.2

What proportion of individuals with 4% of the drug in the bloodstream will have a reaction time in excess of 3 seconds?

Well, so far I have substituted in (x = 4) into the equation to get

E(y) = 3.1

I'm not sure how to calculate the proportion. Could somebody help me?
 

CB

Super Moderator
#3
Hi Alan,

It looks to me like a basic z-value problem. Given an expected value/mean of 3.1 and a standard deviation of 0.2, 0.691 of normally distributed responses will be above 3. I used this normal distribution value calculator.

Does that make sense?