I have the following problem:

I'm given the plot of normal distribution $N(20,36)$.

enter image description here

I am asked to draw the plot of $N(30,20)$ next to it.

I know that the mean is 30, so it's top is going to be on the right. I also know that it has smaller standard deviation so it's going to be more pointy (sharper). When I see it's plot on Minitab, I see that not only it is sharper, but it also has higher probability for the mean.

  • How do I determine how high the plot gets (what's the probability for the mean)?
  • What other advices would you give me for making the second plot as accurate as possible?
  • $\begingroup$ The second question is equivalent to which software or computer program can I use to plot functions? $\endgroup$ – Fakemistake Aug 24 '17 at 9:36
  • $\begingroup$ No, it's not. I have to draw it by hand. I have even stated in the question that I've already drawn it with Minitab and I'm trying to imitate that. $\endgroup$ – Nikola Aug 24 '17 at 9:39
  • $\begingroup$ Table of values $\endgroup$ – Fakemistake Aug 24 '17 at 9:45
  • $\begingroup$ Height increases because total area below the curve is 1. If it is becoming pointy because of lower variance, it has to have more density around mean. If you notice the equation the density at mean is just 1/(sqrt(2*pi)*sigma). That can tell you how high at mean. $\endgroup$ – Bootstrap Aug 24 '17 at 12:06
  • $\begingroup$ @Bootstrap So it's like pressing it from both sides, but still the total area has to be 1 so it's going to become taller. $\endgroup$ – Nikola Aug 24 '17 at 12:18

The pdf is given by $$f(x)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)$$ The maximum value is $f(\mu)$. For the second part you could make a table of values.

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