2024 RI H1 Q12
2024 RI H1 Q12
12 marks
A company makes two kinds of cookies, lemon cookies and chocolate cookies. The mass, in grams, of the two kinds of cookies have independent normal distributions with means and standard deviations as shown in the following table.
| Mean | Standard deviation | |
|---|---|---|
| Lemon | \(32\) | \(0.5\) |
| Chocolate | \(28\) | \(0.6\) |
- Find the probability that the mass of a randomly chosen lemon cookie is more than \(31.5\) grams.[1]
- Find the probability that the total mass of four randomly chosen chocolate cookies is between \(110\) and \(115\) grams.[2]
- Find the probability that total mass of four randomly chosen chocolate cookies differs from thrice the mass of a randomly chosen lemon cookie by less than \(15\) grams.[4]
Lemon cookies are sold at \(\$5\) per \(100\) grams and chocolate cookies at \(\$6\) per \(100\) grams. Dan buys \(10\) lemon cookies and Sophie buys \(10\) chocolate cookies.
- Show that it is almost impossible that Dan pays more than Sophie.[5]
Solution:
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Answer:
(a) \(0.841\). (b) \(0.946\). (c) \(0.301\).
(d) \(3.92\times10^{-9}\); almost impossible under the model.
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