2024 JPJC H1 Q10
2024 JPJC H1 Q10
12 marks
A bakery sells cakes in two different sizes: small and large. The masses, in kg, of the two different sizes of the cakes can be modelled by independent normal distributions. The means and standard deviations of these distributions are shown in the following table.
| Mean | Standard Deviation | |
|---|---|---|
| Small | \(0.22\) | \(0.02\) |
| Large | \(0.45\) | \(0.05\) |
- Find the probability that a randomly chosen small cake has a mass greater than \(0.24\) kg.[1]
- Find the probability that for three randomly chosen small cakes, only one of them has a mass greater than \(0.24\) kg.[3]
- Find the probability that the total mass of \(5\) randomly chosen large cakes is within \(\pm 0.04\) kg of the total mass of \(10\) randomly chosen small cakes.[4]
The cost of producing the cakes is \(\$0.045\) per gram.
- Find the probability that the total cost of producing \(50\) small randomly chosen cakes and \(20\) large randomly chosen cakes is at most \(\$880\).[4]
Solution:
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Answer:(i) \(0.159\). (ii) \(0.337\). (iii) \(0.227\). (iv) \(0.0465\).
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