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Name of student | HENRYTAIGO | Date | |||
Adm. number | Year/grade | HenryTaigo | Stream | HenryTaigo | |
Subject | Probability & Statistics 1 (S1) | Variant(s) | P61, P62, P63 | ||
Start time | Duration | Stop time |
Qtn No. | 1 | 2 | 3 | Total |
---|---|---|---|---|
Marks | 8 | 6 | 7 | 21 |
Score |
Question 1 Code: 9709/61/M/J/18/4, Topic: The normal distribution
$\text{(a)}$ The distance that car tyres of a certain make can travel before they need to be replaced has a normal distribution. A survey of a large number of these tyres found that the probability of this distance being more than $36800 \mathrm{~km}$ is $0.0082$ and the probability of this distance being more than $31000 \mathrm{~km}$ is $0.6915.$ Find the mean and standard deviation of the distribution. $[5]$
$\text{(b)}$ The random variable $X$ has the distribution $\mathrm{N}\left(\mu, \sigma^{2}\right)$, where $3 \sigma=4 \mu$ and $\mu \neq 0$. Find $\mathrm{P}(X<3 \mu)$. $[3]$
Question 2 Code: 9709/62/O/N/18/4, Topic: Permutations and combinations
$\text{(i)}$ Find the number of different ways that 5 boys and 6 girls can stand in a row if all the boys stand together and all the girls stand together. $[3]$
$\text{(ii)}$ Find the number of different ways that 5 boys and 6 girls can stand in a row if no boy stands next to another boy. $[3]$
Question 3 Code: 9709/63/O/N/18/4, Topic: Permutations and combinations
Out of a class of 8 boys and 4 girls, a group of 7 people is chosen at random.
$\text{(i)}$ Find the probability that the group of 7 includes one particular boy. $[3]$
$\text{(ii)}$ Find the probability that the group of 7 includes at least 2 girls. $[4]$