2024 MI H1 Q12

Sweet & Sour Gummies shop has \(2\) best-selling flavoured gummies, namely Apple and Berry. The mass of the gummies of different flavours may be assumed to have independent normal distribution with the following means and standard deviations in grams.

1. Given that \(75\)% of the Apple-flavoured gummies have mass of at most \(6.2\) grams, find the value of \(\sigma\), correct to \(2\) decimal places.[2]

Use \(\sigma = 0.30\) for the rest of the question.

2. Find the probability that the mass of a randomly chosen Apple-flavoured gummy is more than the mass of a randomly chosen Berry-flavoured gummy.[3]

The Apple-flavoured gummies are sold at a price of \$0.035 per gram, while the Berry-flavoured gummies are sold at \$0.039 per gram.

3. Find the probability that the total cost of \(12\) randomly chosen Apple-flavoured gummies and \(20\) randomly chosen Berry-flavoured gummies exceeds \$6.30.[4]