IB Maths AA SL 4.9 Normal Distribution

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise calculating normal probabilities and inverse-normal cut-offs, using symmetry or standardisation and interpreting shaded regions, percentiles and unknown parameters.

How this is tested

translate the verbal event into the correct lower, upper or interval area under the normal curve
standardise with z = (x - μ)/σ or use inverse normal to determine a cut-off or parameter
use symmetry and the 68-95-99.7 rule only when the requested bounds match standard deviations

[Maximum number: 3]

A garden centre sells seeds for two varieties of sunflowers: large and giant.
The heights of large sunflowers are normally distributed with mean $\mu$ and standard deviation $\sigma$ .
It is known that 25 % of large sunflowers have a height of over 180 cm .

Given that $\mu+A \sigma=180$ , where $A \in \mathbb{R}$ , find the value of A.

The heights of giant sunflowers are also normally distributed.
The giant sunflowers have a mean height that is 35 cm more than that of the large sunflowers and a standard deviation that is double that of the large sunflowers.

It is known that 98 % of giant sunflowers have a height greater than 180 cm .

How this is tested

Question 6(a)