2024 NYJC H1 Q12
2024 NYJC H1 Q12
12 marks
In this question, you should state the parameters of any normal distributions you use.
A company produces two electrical components, Type \(X\) and Type \(Y\). The mass, in kilograms, of Type \(X\) and Type \(Y\) components have independent normal distributions. The means and standard deviations of these distributions are shown in the following table.
| Mean | Standard deviation | |
|---|---|---|
| Type \(X\) | \(0.15\) | \(0.02\) |
| Type \(Y\) | \(0.21\) | \(0.05\) |
- Find the probability that the mass of a randomly chosen Type \(X\) component is more than \(6\)% above the mean mass.[2]
- Find the probability that the total mass of \(4\) randomly chosen Type \(X\) components is greater than \(0.65\) kg.[2]
- Find the probability that the total mass of \(4\) randomly chosen Type \(X\) components is within \(\pm 0.05\) kg of the total mass of \(3\) randomly chosen Type \(Y\) components.[4]
The cost of producing a Type \(X\) and Type \(Y\) component are \(\$0.46\) per \(100\) g and \(\$0.52\) per \(100\) g respectively.
- Find the probability that the total cost of \(40\) Type \(X\) components and \(60\) Type \(Y\) components is less than \(\$95\).[4]
Solution:
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Answer:(a) \(0.326\). (b) \(0.106\). (c) \(0.382\). (d) \(0.815\).
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