In a normal approximation to the Wilcoxon signed rank sum test, the test statistic is calculated as z = 1.59. For a two-tail test, the p-value is:

The p-value for a two-tail test with a test statistic of z = 1.59 is calculated as follows:

1. First, we need to find the probability associated with the z-score of 1.59 from the standard normal distribution table or using a z-score calculator. The probability associated with z = 1.59 is approximately 0.9441. This is the area to the left of z = 1.59.

2. Since we are conducting a two-tail test, we are interested in the probability in both tails of the distribution. The area to the right of z = 1.59 is 1 - 0.9441 = 0.0559.

3. Because it's a two-tail test, we need to double this area to account for both tails of the distribution. So, the p-value is 2 * 0.0559 = 0.1118.

So, the p-value for a two-tail test with a test statistic of z = 1.59 is approximately 0.1118.