The normal distributionEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

What does X\sim N(\mu,\sigma^2) mean?
Describe the shape of a Normal curve.
Where are the points of inflection of a Normal curve?
What does a larger \sigma do to the curve?
What is P(X=a) for a Normal variable?
What is P(X<\mu)?
How do you standardise X\sim N(\mu,\sigma^2)?
Symmetry: P(X<\mu-k)=?
X\sim N(42,3^2). Find P(X45).
z-value with P(Z<z)=0.9?
What is z when P(Z<z)=0.975?
How do you find both \mu and \sigma from two probabilities?
What value goes into the calculator for N(5,4)?

Exam questions on The normal distribution

The height, $H$ cm, of a plant of a certain variety is modelled by $H\sim N(42,3^2)$ .
Find the probability that a plant chosen at random has a height between 38 cm and 47 cm.2 marks
Scores on a reasoning test are modelled by $X\sim N(100,15^2)$ .
Find the score that is exceeded by 10% of people.2 marks
The lifetime, $L$ hours, of a type of battery is modelled by $L\sim N(\mu,\sigma^2)$ . It is found that $P(L<200)=0.1$ and $P(L>260)=0.2$ .
Show that $\mu-1.2816\sigma=200$ and $\mu+0.8416\sigma=260$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).