The quantile or probit function, as you can see from the link (see "Computatuon"), is computed with inverse gaussian error function which I hope is downloadable for calculators like TI-89. Look here for instance.

You can check Wan et al. (2014)^*. They build on Bland (2014) to estimate these parameters according to the data summaries available. See scenario C3 in their paper :

$$ \bar{X} ≈ \frac {q_{1} + m + q_{3}}{3}$$

$$ S ≈ \frac {q_{3} - q_{1}}{1.35}$$

or, if you have the sample size :

$$ S ≈ \frac {q_{3} - q_{1}}{2 \Phi^{-1}\left(\frac{0.75n-0.125}{n+0.25}\right) }$$

where is the first quartile, the median, is the 3^rd quartile and the upper z^th percentile of the standard normal distribution.

So, in R :

q1 <- 0.02
q3 <- 0.04
n <- 100

(s <- (q3 - q1) / (2 * (qnorm((0.75 * n - 0.125) / (n + 0.25)))))
#[1] 0.0150441

^{* Wan, Xiang, Wenqian Wang, Jiming Liu, and Tiejun Tong. 2014. “Estimating the Sample Mean and Standard Deviation from the Sample Size, Median, Range And/or Interquartile Range.” BMC Medical Research Methodology 14 (135). doi:10.1186/1471-2288-14-135.}