  In this paper, we introduce a new approximation of the cumulative
distribution function of the standard normal distribution based on Tocher's
approximation. Also, we assess the quality of the new approximation using two
criteria namely the maximum absolute error and the mean absolute error. The
approximation is expressed in closed form and it produces a maximum absolute
error of 4.43*10^(-10) while the mean absolute error is 9.62*10^(-11). In
addition, we propose an approximation of the inverse cumulative function of the
standard normal distribution based on Polya approximation and compare the
accuracy of our findings with some of the existing approximations. The results
show that our approximations surpass other existing ones based on the
aforementioned accuracy measures.
