2025 MI P2 Q6

The waiting times for customers to get their pastries from a popular bakery is modelled by a normal distribution with mean \(\mu\) minutes and standard deviation \(\sigma\) minutes. On average, \(10\%\) of customers wait for more than \(25\) minutes and the same percentage of customers wait for less than \(5\) minutes.

1. Find the values of \(\mu\) and \(\sigma\), leaving your answers to the nearest minute.[3]
2. Explain if the normal distribution is a suitable model for the waiting times for customers to get pastries from this bakery.[1]