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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 Total
Marks 11 10 10 31
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 3 questions Question 1 Code: 9709/72/M/J/19/7, Topic: - All the seats on a certain daily flight are always sold. The number of passengers who have bought seats but fail to arrive for this flight on a particular day is modelled by the distribution$\mathrm{B}(320,0.005)$.$\text{(i)}$Explain what the number 320 represents in this context.$[1]\text{(ii)}$The total number of passengers who have bought seats but fail to arrive for this flight on 2 randomly chosen days is denoted by$X$. Use a suitable approximating distribution to find$\mathrm{P}(2 < X < 6)[3]\text{(iii)}$Justify the use of your approximating distribution.$[2]$After some changes, the airline wishes to test whether the mean number of passengers per day who fail to arrive for this flight has decreased.$\text{(iv)}$During 5 randomly chosen days, a total of 2 passengers failed to arrive. Carry out the test at the$2.5 \%$significance level.$[5]$Question 2 Code: 9709/73/M/J/19/7, Topic: - Each day at a certain doctor's surgery there are 70 appointments available in the morning and 60 in the afternoon. All the appointments are filled every day. The probability that any patient misses a particular morning appointment is$0.04$, and the probability that any patient misses a particular afternoon appointment is$0.05$. All missed appointments are independent of each other. Use suitable approximating distributions to answer the following.$\text{(i)}$Find the probability that on a randomly chosen morning there are at least 3 missed appointments.$[3]\text{(ii)}$Find the probability that on a randomly chosen day there are a total of exactly 6 missed appointments.$[3]\text{(iii)}$Find the probability that in a randomly chosen 10-day period there are more than$50 \mathrm{missed}$appointments.$[3]$Question 3 Code: 9709/73/O/N/19/7, Topic: - Bob is a self-employed builder. In the past his weekly income had mean$\$546$ and standard deviation $\$ 120$. Following a change in Bob's working pattern, his mean weekly income for 40 randomly chosen weeks was$\$581$. You should assume that the standard deviation remains unchanged at $\$ 120$.$\text{(i)}$Test at the$2.5 \%$significance level whether Bob's mean weekly income has increased.$[5]$Bob finds his mean weekly income for another random sample of 40 weeks and carries out a similar test at the$2.5 \%$significance level.$\text{(ii)}$Given that Bob's mean weekly income is now in fact$\$595$, find the probability of a Type II error. $[5]$

Worked solutions: P1, P3 & P6 (S1)

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