Paper 2 Section B Practice: Normal Distribution

Original practice material

These questions total 20 marks. State each derived normal distribution before using it.

Answers: Normal Distribution Answers.

Question 1: packet masses

The mass $X$ grams of a packet is modelled by

$$X\sim N(505,6^2).$$

(a) Find $P(498<X<514)$. [3]

(b) Find the value $a$ such that $P(X<a)=0.02$. [3]

(c) Two packets are selected independently. Find the probability that their total mass is less than $1000$ g. [4]

Question 2: difference and weighted total

Independent random variables $A$ and $B$ satisfy

$$A\sim N(40,5^2),B\sim N(32,4^2).$$

(a) State the distribution of $A-B$. [2]

(b) Find $P(A-B>15)$. [3]

(c) Let $W=2A+3B$. Find $E(W)$ and $\mathrm{Var}(W)$. [3]

(d) Find the value $w$ such that $P(W>w)=0.10$. [2]