Brown sugar is packed in bags to be sold. The masses of brown sugar in the bags (in kg) are normally

Question

Brown sugar is packed in bags to be sold. The masses of brown sugar in the bags (in kg) are normally distributed with mean $\mu $ and variance ${{\sigma }^{2}}$. It is known that $\mathrm{30 }\!\!%\!\!\mathrm{ }$ of the bags of brown sugar have masses which differ from $\mu $ by at least $c$ kg. Find the probability that a randomly chosen bag of brown sugar has a mass which differs from $\mu $ by less than $~2c$ kg. [4] In this question you should state clearly all the distributions that you use, together with the values of the appropriate parameters. The weight of a bar of Brand $A$ soap is normally distributed with mean $180$g and standard deviation $10$g. The weight of a bar of Brand $B$ soap is normally distributed with mean $240$g and standard deviation $20$g. Find the probability that the total weight of $3$ randomly chosen bars of brand $A$ soap is more than twice the weight of a randomly chosen bar of brand $B$ soap. State an assumption needed for your calculations. [4] Brand $A$ soap are sold at $\$2$ per $100$g. Brand $A$ soaps are randomly selected and packed in boxes of $100$each. Find the probability that, in one box, more than $10$ bars cost more than $\$3.80$ each. [3]

Accepted Answer

(a) 0.962; (b)(i) 0.916; (b)(ii) 0.935

2022 ACJC J2 MYE Q12

2022 ACJC J2 MYE Q12

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