At a supermart, the option of using cashless payment for purchases is available to customers. On ave

Question

At a supermart, the option of using cashless payment for purchases is available to customers. On average, $p\%$ of the customers use cashless payment.

The manager of the supermart selects a sample of $30$ customers for a survey.

The probability of not more than $1$ of customers surveyed use cashless payment for their purchases is $\mathrm{0}\mathrm{.245}$. Write down an equation in terms of $p$. Find $p$, giving your answer correct to $3$ decimal places.[3]

For the remaining parts of this question, use $p=30$.

Find the probability that the last customer of the $30$ selected for survey is the ${{10}^{\mathrm{th}}}$ customer who uses a cashless payment for his purchase.[2]

Another manager of the supermart also selects a sample of $30$ customers.

Given that there are a total of less than $16$ customers using cashless payment for their purchases from both samples, find the probability that one of the sample has more than $12$ customers using cashless payment for their purchases.[3]
State one assumption you have made in the calculation in part (iii).
[1]

Accepted Answer

(i) ${\mathrm{8}\mathrm{.811}}$ (ii) $\approx \mathrm{0}\mathrm{.0472}$ (iii) $\approx \mathrm{0}\mathrm{.000831}$ (iv) The assumption is that the people being surveyed are all different in both samples. (OR Samples are independently 	ext{ and } identically distributed.)

2018 RVHS P2 Q7

2018 RVHS P2 Q7

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