In this question you should, where applicable, state clearly all the distributions that you use, tog

Question

In this question you should, where applicable, state clearly all the distributions that you use, together with the values of the appropriate parameters. A supermarket produces its own packs of white sesame seeds and fennel seeds for sale under its house brand. The masses (in grams) of a randomly chosen pack of white sesame seeds and that of a randomly chosen pack of fennel seeds, denoted by $W$ and $F$ respectively, have independent normal distributions. The means and standard deviations of these distributions are shown in the following table Mass of a pack ofMean (g)Standard deviation (g) white sesame seeds $({W})$$250$${\sigma}$ fennel seeds $({F})$$300$$2.5$ It is given that $5\%$ of the packs of white sesame seeds have a mass of less than $245$. Show that the value of $\sigma $ is $\mathrm{3}\mathrm{.0398}$, correct to $5$ significant figures.[2] Find the probability that the total mass of six randomly chosen packs of white sesame seeds is less than five times the mass of a randomly chosen pack of fennel seeds by not more than $20$ grams.[3] $n$ packs of white sesame seeds and $n$ packs of fennel seeds are chosen at random. Find the smallest value of $n$ such that the probability that the mean mass of these $2n$ packs being at least $278$grams is less than $0.015$.[4]

Accepted Answer

(b) ${0.415}$ ($3$ s.f.) (c) Smallest value of ${n = 3}$.

Mass of a pack of	Mean (g)	Standard deviation (g)
white sesame seeds \(({W})\)	\(250\)	\({\sigma}\)
fennel seeds \(({F})\)	\(300\)	\(2.5\)

2023 HCI P2 Q10

2023 HCI P2 Q10

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