IB Maths AA SL 4.12 Standardizing Normal Variables Questions

Practise IB Mathematics SL 4.12 by applying standardizing normal variables methods to questions from the Question Bank.

Exam points

Standardize a normal variable with z = (x − μ)/σ and interpret z as the number of standard deviations from the mean.
Use z-values with a normal model to find an unknown mean or standard deviation from a stated observation or probability condition.

[Maximum number: 4]

A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.

The probability that the reaction time of a person in Group Y is greater than 0.65 seconds is 0.396 . Find the value of $\sigma$ .

In the study, 38 % of the participants are in Group X.

correct z-value
0.263714...
evidence of appropriate approach
eg $\quad \frac{0.65-0.592}{\sigma}, 0.264=\frac{x-\mu}{\sigma}$
correct substitution
eg $\quad 0.263714=\frac{0.65-0.592}{\sigma}, \sigma=\frac{0.65-0.592}{0.264}$
0.219934
$\sigma=0.220$

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IB Maths AA SL 4.12 Standardizing Normal Variables Questions question 1