2015 VJC P2 Q11
2015 VJC P2 Q11
Prelims
Free
A supermarket sells \(2\) different types of apples – Granny Smith and Fuji. The masses, in grams, of each type of apples follow normal distributions. The means and standard deviations of these distributions are shown in the following table.
| Mean (g) | Standard deviation (g) | |
|---|---|---|
| Granny Smith | 150 | 11.7 |
| Fuji | 180 | 15.2 |
- Two Fuji apples are chosen. Find the probability that their masses differs by at least \(20\) g.
- Granny Smith apples are sold at \(\$3.50\) per kg and Fuji apples at \(\$5\) per kg.
Find the probability that six Granny Smith apples and four Fuji apples cost more than \(\$6.50\).
- State an assumption needed for your calculations in parts (i) and (ii).
Video Solution:
Default solution
For the independent apple masses, every variance contribution is added: \(\operatorname{Var}(C)=6(3.5/1000)^2(11.7)^2+4(5/1000)^2(15.2)^2=0.033165415\). The isolated minus sign before the last Fuji term is a slip; the subsequent calculation uses addition.
Answer:(i) \(0.352\) (ii) \(0.915\) (iii) The masses of all selected apples are independent.
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