Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
Nov 2013 p61 q1
3152
It is given that \(X \sim N(30, 49)\), \(Y \sim N(30, 16)\) and \(Z \sim N(50, 16)\). On a single diagram, with the horizontal axis going from 0 to 70, sketch three curves to represent the distributions of \(X, Y\) and \(Z\).
Solution
The normal distribution \(X \sim N(30, 49)\) has a mean of 30 and a variance of 49, which means it is wider and shorter compared to \(Y\) and \(Z\). The curve for \(X\) should be centered at 30 and spread roughly from 10 to 50.
The normal distribution \(Y \sim N(30, 16)\) has the same mean as \(X\) but a smaller variance, making it taller and narrower. The curve for \(Y\) should also be centered at 30 but be higher and thinner than \(X\).
The normal distribution \(Z \sim N(50, 16)\) has a mean of 50 and the same variance as \(Y\). The curve for \(Z\) should be the same shape as \(Y\) but centered at 50.