In this question you should state the parameters of any distributions you use. A drinks stall specia

Question

In this question you should state the parameters of any distributions you use. A drinks stall specialises in fruit smoothies, which contain apples. The apples used by the stall have masses, in grams, that follow the distribution $\mathrm{N}(100, 6^2)$. Find the probability that the mass of a randomly chosen apple is no more than $105$ grams.[1] Before the apples can be blended, they need to be prepared by peeling them and removing their cores. This preparation process reduces the mass of each apple by $30$%. Find the probability that the mass of a randomly chosen apple, after preparation, is more than $78$ grams.[3] The stall sells its Signature smoothie, which uses $2$ prepared apples, $1$ peeled banana and $12$ blackcurrants; all of these are randomly chosen. The stall also adds a fixed $50$ grams of milk before blending everything together. You should ignore any changes in mass from the blending process. * The masses of peeled bananas, in grams, follow the distribution $\mathrm{N}(130, 8^2)$. * The masses of blackcurrants, in grams, follow the distribution $\mathrm{N}(2.5, 0.6^2)$. $90$% of the Signature smoothies have a mass of at least $m$ grams. Find the value of $m$.[4] A teacher purchases $25$ Signature smoothies for her form class. Find the probability that at least $20$ of the Signature smoothies have masses between $330$ and $360$ grams.[3] The stall also makes blackcurrant smoothies using $n$ blackcurrants and a fixed $175$ grams of milk. Find the smallest value of $n$ such that the probability of the mass of a blackcurrant smoothie exceeding $300$ grams is at least $0.95$.[3]

Accepted Answer

(a)$P(X\leq 105)=0.798$ (b)$P(Y>78)=0.0284$ (c)m=337 (d)$P(R\geq 20)=0.677$ (e) least value of n is 53.

2025 EJC P2 Q10

2025 EJC P2 Q10