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### HENRYTAIGO

#### Cambridge International AS and A Level

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

Qtn No. 1 2 3 4 Total
Marks 10 14 10 10 44
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 4 questions Question 1 Code: 9709/71/M/J/13/7, Topic: - Leila suspects that a particular six-sided die is biased so that the probability,$p$, that it will show a six is greater than$\frac{1}{6}$. She tests the die by throwing it 5 times. If it shows a six on 3 or more throws she will conclude that it is biased.$\text{(i)}$State what is meant by a Type I error in this situation and calculate the probability of a Type I error.$[3]\text{(ii)}$Assuming that the value of$p$is actually$\frac{2}{3}$, calculate the probability of a Type II error.$[3]$Leila now throws the die 80 times and it shows a six on 50 throws.$\text{(iii)}$Calculate an approximate$96 \%$confidence interval for$p$.$[4]$Question 2 Code: 9709/73/M/J/13/7, Topic: - In the past the weekly profit at a store had mean$\$34600$ and standard deviation $\$ 4500$. Following a change of ownership, the mean weekly profit for 90 randomly chosen weeks was$\$35400$.

$\text{(i)}$ Stating a necessary assumption, test at the $5 \%$ significance level whether the mean weekly profit has increased. $[6]$

$\text{(ii)}$ State, with a reason, whether it was necessary to use the Central Limit theorem in part $\text{(i)}$. $[2]$

The mean weekly profit for another random sample of 90 weeks is found and the same test is carried out at the $5 \%$ significance level.

$\text{(iii)}$ State the probability of a Type I error. $[1]$

$\text{(iv)}$ Given that the population mean weekly profit is now $\$ 36500$, calculate the probability of a Type II error.$[5]$Question 3 Code: 9709/71/O/N/13/7, Topic: - Kieran and Andreas are long-jumpers. They model the lengths, in metres, that they jump by the independent random variables$K \sim \mathrm{N}(5.64,0.0576)$and$A \sim \mathrm{N}(4.97,0.0441)$respectively. They each make a jump and measure the length. Find the probability that$\text{(i)}$the sum of the lengths of their jumps is less than$11 \mathrm{~m}$,$[4]\text{(ii)}$Kieran jumps more than$1.2$times as far as Andreas.$[6]\$

Question 4 Code: 9709/72/O/N/13/7, Topic: -

Worked solutions: P1, P3 & P6 (S1)

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