CAIE A-Level Mathematics A2 6.4.3 Sample Mean Questions

Practise treating a sample mean as a random variable and applying its expectation and variance when samples are taken from a population.

[Maximum number: 3]

In a large population, the systolic blood pressure (SBP) of adults is normally distributed with mean 125.4 and standard deviation 18.6.

The SBP of 12-year-old children in the same population is normally distributed with mean 117. Of these children 88\% have SBP more than 108.

Find the standard deviation of this distribution.

Three adults are chosen at random from this population.

$\frac{108-117}{\sigma}=-1.175$ $1.1749<z \leqslant 1.175$ or $-1.175 \leqslant z<-1.1749$
108 and 117 substituted in ± standardisation formula, no continuity
correction, not $\sigma^{2}, \sqrt{ } \sigma$ , equated to a z-value.

$\sigma=7.66$ $7.659 \leqslant \sigma \leqslant 7.66$
If M0 scored, SC B1 for $7.659 \leqslant \sigma \leqslant 7.66$

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CAIE A-Level Mathematics A2 6.4.3 Sample Mean Questions question 1