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#### Cambridge International AS and A Level

 Name of student GRADYACIFS Date Adm. number Year/grade 1993 Stream Gradyacifs Subject Probability & Statistics 2 (S2) Variant(s) P71, P72, P73 Start time Duration Stop time

Qtn No. 1 2 3 4 Total
Marks 5 6 8 8 27
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 4 questions Question 1 Code: 9709/71/M/J/13/3, Topic: - Weights of cups have a normal distribution with mean$91 \mathrm{~g}$and standard deviation$3.2 \mathrm{~g}$. Weights of saucers have an independent normal distribution with mean$72 \mathrm{~g}$and standard deviation$2.6 \mathrm{~g}$. Cups and saucers are chosen at random to be packed in boxes, with 6 cups and 6 saucers in each box. Given that each empty box weighs$550 \mathrm{~g}$, find the probability that the total weight of a box containing 6 cups and 6 saucers exceeds$1550 \mathrm{~g}$.$[5]$Question 2 Code: 9709/73/M/J/13/3, Topic: - Each of a random sample of 15 students was asked how long they spent revising for an exam. The results, in minutes, were as follows. $$\begin{array}{lllllllllllllll} 50 & 70 & 80 & 60 & 65 & 110 & 10 & 70 & 75 & 60 & 65 & 45 & 50 & 70 & 50 \end{array}$$ Assume that the times for all students are normally distributed with mean$\mu$minutes and standard deviation 12 minutes.$\text{(i)}$Calculate a$92 \%$confidence interval for$\mu$.$[4]\text{(ii)}$Explain what is meant by a$92 \%$confidence interval for$\mu$.$[1]\text{(iii)}$Explain what is meant by saying that a sample is 'random'.$[1]$Question 3 Code: 9709/71/O/N/13/3, Topic: - Following a change in flight schedules, an airline pilot wished to test whether the mean distance that he flies in a week has changed. He noted the distances,$x \mathrm{~km}$, that he flew in 50 randomly chosen weeks and summarised the results as follows. $$n=50 \quad \Sigma x=143~300 \quad \Sigma x^{2}=410~900~000$$$\text{(i)}$Calculate unbiased estimates of the population mean and variance.$[3]\text{(ii)}$In the past, the mean distance that he flew in a week was$2850 \mathrm{~km}$. Test, at the$5 \%$significance level, whether the mean distance has changed.$[5]\$

Question 4 Code: 9709/72/O/N/13/3, Topic: -

Worked solutions: P1, P3 & P6 (S1)

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