Standard normal distribution with parameter which modifies Variable Z

Question

I am sitting over the following example:

Let Z be normally distributed, ie Z ~ N (0.1). Find K such that

P(Z / K + 2 <0) = 0.29 and K < 0.

I don't understand what should I do with parameter K. Obviously K modifies the distribution trough the standard deviation. But in this case Z/K is not standard normal distributed. Can somebody help me how to start solving this example?

Answer 1

You can modify: $$P\left(\frac{Z}{K} + 2 <0\right) = 0.29 \stackrel{K<0}\Rightarrow P\left(Z>-2K\right) = 0.29 \Rightarrow -2K=0.5534 \Rightarrow K=-0.2767.$$