2024 SAJC H1 Q11

In this question you should, where applicable, state clearly all the distributions that you use, together with the values of the appropriate parameters.
Andrew is a chef who specialises in baking cookies and cakes. The time taken, in minutes, by Andrew to bake cookies and cakes have independent normal distributions with means and standard deviations as shown in the table below.

1. It is given that Andrew takes no more than \(t\) minutes to bake \(80\)% of the cakes. Find the value of \(t\).[3]
2. Find the probability that Andrew takes less than \(300\) minutes to bake a total of \(4\) cookies and \(5\) cakes.[4]

Compared to Andrew, another chef, Jane, takes \(20\)% more time to bake a cake and \(15\)% more time to bake a cookie.

3. Find the probability that Jane takes more time to bake \(2\) randomly chosen cakes than to bake \(6\) randomly chosen cookies.[4]