N2007 P2 Q8 [Modified]
N2007 P2 Q8 [Modified]
Past Year National Exams
Free
Chickens and turkeys are sold by weight. The masses, in kg, of chickens and turkeys are modelled as having independent normal distributions with means and standard deviations as shown in the table.
Mean mass | Standard deviation | |
|---|---|---|
Chickens | \(2.2\) | \(0.5\) |
Turkeys | \(10.5\) | \(2.1\) |
Chickens are sold at \(\$3\) per kg and turkeys at \(\$5\) per kg.
- Find the probability that a randomly chosen chicken has a selling price exceeding \(\$7\).
- Find the probability of the event that both a randomly chosen chicken has a selling price exceeding \(\$7\) and a randomly chosen turkey has a selling price exceeding \(\$55\).
- Find the probability that the total selling price of a randomly chosen chicken and a randomly chosen turkey is more than \(\$62\).
- Explain why the answer to part (iii) is greater that the answer to part (ii).
- Find the probability that the cost of sixteen chickens is more than the cost of \(2\) turkeys.
Video Solution:
Default solution
Answer:(i) \(0.395\) (ii) \(0.160\) (iii) \(0.392\) (iv) The event in (ii) is a proper subset of the event in (iii), so the probability in (iii) is greater. (v) \(0.515\)
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