It is known that the probability of a customer using e-payment at a hawker stall is $0.25$. A grou

Question

It is known that the probability of a customer using e-payment at a hawker stall is $0.25$. A group of customers is chosen at random, find the probability that the ${{7}^{\mathrm{th}}}$ chosen customer is the ${{5}^{\mathrm{th}}}$ customer using e-payment at the hawker stall.[3] A sample of $40$ customers were randomly chosen from the hawker stall each day. In a month of $30$ days, find the probability that there is at least $15$ days with at most $10$ customers per sample making e-payment.[3] The probability that a hawker uses the online delivery platform Foodgowhere is $p$. A random sample of $~n$ hawkers is taken and the random variable $X$ denotes the number of hawkers in the sample that uses Foodgowhere. Explain what is meant by a random sample in this context.[1] Assuming that $X$ follows a binomial distribution. It is given that $\mathrm{P}\left( X\le 1 \right)=\mathrm{0}\mathrm{.05303}$ and the expected number of hawkers using Foodgowhere is $3.96$. Write down two equations satisfied by $p$ and $~n$. Hence find the value of $p$ and $~n$.[3] Given that $n=15$, find the set of values of $p$ so that that the most likely number of hawkers in the sample who uses Foodgowehere is $5$.[3]

Accepted Answer

(a)(i) ${0.00824	ext{ (3 s.f.)}}$ (ii) ${0.868	ext{ (3 s.f.)}}$ (b)(i) A random sample in this context means that each hawker has an equal chance of being selected for the sample and the selection of one hawker is independent of any other hawkers. (ii) ${n=11}$ (nearest integer) (iii) ${\frac{5}{16} < p < \frac{3}{8}}$

2022 ACJC P2 Q11

2022 ACJC P2 Q11

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