2025 Nov TZ1 P2 Q2

The random variable \(\mathrm{Z}\) has a standard normal distribution with mean \(0\) and standard deviation \(1\).

1. Find \(\mathrm{P(Z} < 1.7)\).

   [1]

It is known that \(\mathrm{P}(a < \mathrm{Z} < 1.7) = 0.7865\), correct to four significant figures.

2. Sketch this information on the following diagram.

   [1]
   

3. Hence, or otherwise, find the value of \(a\).

   [2]