Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
For a large population, adults’ systolic blood pressure (SBP) follows a normal distribution with mean $125.4$ and standard deviation $18.6$.
(a)[2]
Find the probability that a randomly chosen adult has SBP below $132$.
(b)[3]
The SBP of $12$-year-old children in the same population has a normal distribution with mean $117$. Of these children, $88\%$ have SBP above $108$.
Find the standard deviation of this distribution.
(c)[4]
Three adults are selected at random from this population.
Find the probability that all three of these adults have SBP within $1.5$ standard deviations of the mean.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate standardisation, for example $P(X<132)=P\\left(Z<\\frac{132-125.4}{18.6}\\right)$ (continuity correction allowed).” …