The weight, $Y$, of a Yummy cereal bar is normally distributed with mean $\left( 120-k \right)$g and

Question

The weight, $Y$, of a Yummy cereal bar is normally distributed with mean $\left( 120-k \right)$g and standard deviation 10g. The weight, F, of a Fullness cereal bar is normally distributed with mean 180 g and standard deviation 20 g. Given that $\mathrm{P}\left( Y150 \right)$, show that the value of $k$ is 5. [1] 5 Yummy cereal bars are randomly chosen. Find the probability that exactly one bar weighs lesser than the lower quartile weight and exactly one bar weighs more than the median weight. [2] Find the probability that the weight of 2 randomly chosen Yummy cereal bars differs from one and a half times the weight of a randomly chosen Fullness cereal bar by at most 5g. State the assumption needed for your working. [4] The Fullness cereal bars are sold at $2 per 100g. Find the probability that a randomly chosen Fullness cereal bar costs more than $3.50. [2] A random sample of 100 Fullness cereal bars is taken. Find the probability that there are at least 55 bars but at most 65 bars with each costing more than $3.50. [3]

Accepted Answer

(i) k = 5; (ii) 5/128; (iii) 0.0582; (iv) 0.599; (v) 0.738

2010 PJC P2 Q12

2010 PJC P2 Q12

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