There is a virus codenamed Covid-Pi spreading across the world. It is highly contagious and causes high mortality rates. A Multi-Ministry Taskforce is set up to tackle the Covid-Pi pandemic.

In order to decide the quarantine period for people who are at risk having Covid-Pi virus, the Taskforce must know the incubation period of the virus, i.e., how long it causes a person to show symptom after he has contacted the virus.

Worldwide Statistics shows that the incubation periods follow a Normal Distribution with a mean of 12 days and a standard deviation of 5 days.

(i) Find the incubation period that only 3% of the Covid-Pi virus will last beyond before showing symptom in human bodies.

(ii) The Taskforce takes a sample of 15 airport arrival passengers who are tested positive for Covid-Pi virus. Evaluate the probability that the mean of their virus incubation periods will be more than 10 days. Explain why this analysis can be conducted on a small sample size.

**Note: In Q(a)(i) & (ii), you shall use relevant Statistics formula and Standard Normal Distribution table to derive the answers.