2022 DHS P2 Q10
In this question you should state the parameters of any distributions that you use.
A fruit stall vendor sells rock melons and watermelons. The masses (in grams) of a randomly chosen rock melon and watermelon, denoted by $X$ and $Y$ respectively, have independent normal distributions. The means and standard deviations of these distributions are shown in the following table.
(a)
Sketch the distribution of $X$ for masses between $558$ g to $646$ g.
[1]
(b)
Find the expected number of rock melons with mass more than $600$ g from $300$ randomly chosen rock melons.
[2]
(c)
Comment whether the combined masses of the melons of both types is normally distributed.
[1]
Rock melons and watermelons are priced at $\$3$/kg and $\$2.80$/kg respectively.
(d)
Find the probability that the mean selling price of $4$ randomly chosen rock melons differs from the selling price of a randomly chosen watermelon by at most $60$ cents.
[4]
(e)
Ah Guan buys $20$ melons, $n$ of them are rock melons and the rest are watermelons. Find the greatest value of $n$ such that the probability that the total cost of these $20$ melons exceeding $\$38$ is more than $0.95$. You should show your working clearly.
[4]
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