In order to calculate the conversion of z score to percentile we need to get the cumulative area under the normal distribution curve. We could manually calculate the numeric integral however this might lead us to mistaken results. The best way to do it is by using existing modules written by some trusty source.
In the case of Java, I used NormalDistribution class which comes as part of the Apache Commons Math jar.
zScore: 1.6151417880272858 Percentile: 94.68600033649766