A grocery store sells two types of apples, Brand $A$ and Brand $S$. The masses (in grams) of the

Question

A grocery store sells two types of apples, Brand $A$ and Brand $S$. The masses (in grams) of the apples for each brand can be modelled by independent normal distributions with means and standard deviations as shown in the table

	Mean	Standard Deviation
Brand $A$	$82.2$	$2.2$
Brand $S$	$78.8$	$3.1$

You may assume that the following samples of apples are randomly chosen.

Find the probability that the mass of a Brand $A$ apple is between $80$ grams and $84$ grams.[1]
Find the probability that the total mass of five Brand $A$ apples is more than $408$ grams.[3]
The mass of a peeled apple is $90\%$ of its original mass. Find the probability that the difference in mass between a Brand $S$ apple and a peeled Brand $A$ apple exceeds one gram.
[5]

Accepted Answer

(a) ${0.635}$ ($3$ s.f.) (b) ${0.729}$ ($3$ s.f.) (c) ${0.907}$ ($3$ s.f.)

	Mean	Standard Deviation
Brand \(A\)	\(82.2\)	\(2.2\)
Brand \(S\)	\(78.8\)	\(3.1\)

2023 TMJC P2 Q8

2023 TMJC P2 Q8

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