CAIE A-Level Mathematics A2 6.2.1 Normal Distribution Questions

Practise finding distributions of sums and differences of independent normal variables.

Exam points

find the mean and variance of sums of independent normal variables
model combined measurements with normal distributions
calculate probabilities for sums and differences using standardisation

[Maximum number: 5]

The masses in kilograms of large and small bags of cement have the independent distributions N(50,2.4) and N(26,1.8) respectively.

Find the probability that the total mass of 5 randomly chosen large bags of cement is greater than the total mass of 10 randomly chosen small bags of cement.

$D\sim N\bigl(5\times50-10\times26,\;5\times2.4+10\times1.8\bigr)=N(-10,30)$ $z=\frac{0-(-10)}{\sqrt{30}}=1.826$ $P(D>0)=1-\Phi(1.826)=0.0339\approx0.0340$

Award marks for the distribution, variance, standardisation and tail probability;
final answer 0.0339 or 0.0340 to 3 significant figures.

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CAIE A-Level Mathematics A2 6.2.1 Normal Distribution Questions question 1