In this question you should state clearly the values of the parameters of any normal distributions t

Question

In this question you should state clearly the values of the parameters of any normal distributions that you use. In a botanical study, the masses of various types of plants are analysed. The masses, in grams, of Type A plants and Type B plants can be modelled by independent normal distributions. The means and standard deviations of these distributions are shown in the following table. MeanStandard deviation Type A$200$$10$ Type B$175$$8$ It is $95$% certain that $6$ Type A plants chosen at random have a total mass exceeding $L$ grams. Find the value of $L$, correct to $1$ decimal place.[2] Find the probability that the total mass of two randomly chosen Type A plants is within $40$ grams of twice the mean mass of the Type B plants.[3] A specific experiment requires the use of $6$ Type A plants and $8$ Type B plants. The experiment preparation process reduces the mass of each Type A plant by $7$% and the mass of each Type B plant by $5$%. Find the probability that the total mass, after preparation, of $6$ randomly chosen Type A plants and $8$ randomly chosen Type B plants is at least $2.4$ kilograms.[3] Type A plants are sold at $\$20$ per $100$ grams, and Type B plants are sold at $\$17.50$ per $100$ grams in a plant nursery. Let $W$ represent the mass of a randomly chosen Type A plant, and $V$ represent the mass of a randomly chosen Type B plant. Find $\mathrm{P}(3(0.2W) - 0.175(V_1 + V_2) > 57)$ and explain in the context of this question what your answer represents.[4]

Accepted Answer

(a)L=1159.7 (b)0.240 (c)0.929 (d)0.609

2024 ASRJC H1 Q12

2024 ASRJC H1 Q12