In this question, you should state the parameters of any normal distributions you use. A confectiona

Question

In this question, you should state the parameters of any normal distributions you use. A confectionary bakes egg tarts for sale. The masses of these egg tarts have a normal distribution and $26$% of them have a mass greater than $65$ grams. An egg tart is equally likely to have a mass less than $50$ grams as it is to have a mass greater than $70$ grams. Find the mean and variance of this distribution.[3] The confectionary also bakes donuts and buns. The masses in grams of the donuts have the distribution $\mathrm{N}(80, 10^2)$ and the masses in grams of the buns have the distribution $\mathrm{N}(70, 6^2)$. Find the probability that the mass of a randomly chosen donut is within $5$ grams from its mean.[1] Find the probability that the mass of a randomly chosen bun is less than the mass of a randomly chosen donut.[2] The confectionary also tops its donuts and buns with chocolate. A chocolate topping increases the mass of a donut by $10$% and the mass of a bun by $20$%. Find the probability that the total mass, with chocolate topping, of $3$ randomly chosen donuts and $5$ randomly chosen buns exceeds $700$ grams.[4]

Accepted Answer

(a)$\mu =60$,$\sigma^2=60.4$ (b)0.383 (c)0.804 (d)0.261

2025 YIJC P2 Q9

2025 YIJC P2 Q9