In this question you should state clearly the values of the parameters of any normal distribution(s)

Question

In this question you should state clearly the values of the parameters of any normal distribution(s) that you use. Papayas and watermelons are sold by weight. The masses, in kg, of papayas and watermelons are modelled as having normal distributions with means and standard deviations as shown in the table. Mean massStandard deviation Papayas${1.85}$$0.12$ Watermelons${6.50}$$0.72$ Sketch the distribution for the masses of papayas between $1.4$kg and $2.3$kg.[2] Find the probability that the mass of a randomly chosen papaya is less than $1.7$kg.[1] Find the probability that the mass of a randomly chosen watermelon exceeds the mass of a randomly chosen papaya by more than $4.5$kg.[3] The mean mass of $n$ randomly chosen watermelons is denoted by $\bar{Y}$ kg. Given that $\mathrm{P}\left( \bar{Y}>k \right)=0.2$, express $k$ in terms of $n$.[3] Papayas are sold at $\$2.20$ per kg and watermelons at $\$1.45$ per kg. Calculate the probability that the total selling price of $3$ randomly chosen papayas and $4$randomly chosen watermelons exceed $\$50$.[3] State an assumption for your calculations in parts (iii), (iv) and (v).[1]

Accepted Answer

(ii) ${0.106}$ ($3$ s.f.) (iii) ${0.581}$ ($3$ s.f.) (iv) ${6.5+\frac{0.606}{\sqrt{n}}}$ (v) ${0.483}$

2024 TMJC P2 Q10

2024 TMJC P2 Q10

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Solution:

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	Mean mass	Standard deviation
Papayas	\({1.85}\)	\(0.12\)
Watermelons	\({6.50}\)	\(0.72\)