IB Maths AA SL 4.12 Standardising Normal Variables

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise converting normal values to z-scores and using probability statements or inverse normal results to determine thresholds, unknown means and standard deviations.

How this is tested

standardise a value with z = (x - μ)/σ and interpret its distance and direction from the mean
translate a tail probability into the correctly signed inverse-normal z-value
form simultaneous z-score equations from two probabilities to determine μ and σ

[Maximum number: 4]

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 .

Determine $\mu$ and $\sigma$ .

How this is tested

Question 6(b)