Find a sample size for a central normal interval

$\bar X\sim N(\mu,1/n)$ exactly and $Z=(\bar X-\mu)/(1/\sqrt n)\sim N(0,1)$. Thus the event is $-0.1\sqrt n<Z<0.1\sqrt n$.

A central area 0.95 leaves 0.025 in each tail. The source’s DISTR → invNorm, area .95, μ 0, σ 1, CENTER gives $\pm1.959963986$. To make the probability strictly larger, $0.1\sqrt n>1.959963986$, hence $n>384.1458821$. The least integer is 385. The source rounds the intermediate bound to 384.14; it leads to the same integer.

Enter $Y_1=\operatorname{normalcdf}(-0.1\sqrt X,0.1\sqrt X,0,1)$ and inspect integer $X=n$. The printed table is:

At 384 the unrounded value is 0.9499564788, below .95 despite its display rounding. At 385 it is 0.9502540093. Monotonic widening of the central interval proves 385 is minimal.