4.9 Normal distributionIB Maths: Applications and Interpretation HL: Flashcards

What these 14 flashcards ask

What do the symbols in X\sim N(\mu,\sigma^2) mean?
Name three properties of the normal curve.
What is P(X=a) for a normal variable?
What percentage lies within \mu\pm\sigma?
What percentage lies within \mu\pm2\sigma?
What percentage lies within \mu\pm3\sigma?
What percentage lies above \mu+\sigma?
How do you find P(Xa) on a GDC?
Inputs for normal cdf?
What area does inverse normal use?
If P(Xk)=0.1, which area do you enter into inverse normal?
What does a larger standard deviation do to the curve?
How do you turn a probability into an expected number?
Give a natural example of a normal distribution.

Exam questions on 4.9 Normal distribution

The mass of rice in a packet is normally distributed with mean $500$ g and standard deviation $8$ g.
Use your GDC to find the probability that a packet has a mass less than $490$ g.2 marks
The time, $T$ minutes, taken by a commuter train to complete its journey is normally distributed with mean $42$ and standard deviation $6$ .
Use your GDC to find the probability that a journey takes between $40$ and $45$ minutes.2 marks
The mass, $M$ grams, of eggs from a farm is normally distributed with mean $62$ and standard deviation $3$ . The eggs are sold in boxes of $240$ .
Use your GDC to find the probability that an egg has a mass greater than $67$ g. Hence find the expected number of eggs in a box that are heavier than $67$ g.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).