Easy -1.8 This is a straightforward sketching task requiring only recall of how normal distribution parameters affect curve shape and position. Students need to know that the mean determines center position and variance affects spread—no calculations, problem-solving, or conceptual depth required.
1 It is given that \(X \sim \mathrm {~N} ( 30,49 ) , Y \sim \mathrm {~N} ( 30,16 )\) and \(Z \sim \mathrm {~N} ( 50,16 )\). On a single diagram, with the horizontal axis going from 0 to 70 , sketch three curves to represent the distributions of \(X , Y\) and \(Z\).
\(Z\) same shape as \(Y\) but mean at 50, ft wrong \(Y\)
B1ft [3]
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $X$ mean at 30, roughly from 10 to 50 or 15–45 | B1 | |
| $Y$ same mean as $X$ but higher and thinner | B1 | |
| $Z$ same shape as $Y$ but mean at 50, ft wrong $Y$ | B1ft **[3]** | |
---
1 It is given that $X \sim \mathrm {~N} ( 30,49 ) , Y \sim \mathrm {~N} ( 30,16 )$ and $Z \sim \mathrm {~N} ( 50,16 )$. On a single diagram, with the horizontal axis going from 0 to 70 , sketch three curves to represent the distributions of $X , Y$ and $Z$.
\hfill \mbox{\textit{CAIE S1 2013 Q1 [3]}}