Task:
The automatic machine stamps parts, the length of which is practically reliably contained in the range from $49.7$ to $50.3$ mm. A part is recognized as standard if the deviation of its length from the nominal, equal to $50$ mm, does not exceed $0.25$ mm. Find the percentage of defects in products manufactured by the machine.
Solution:
Let the $\xi$ - automatic machine stamps parts params, and $\delta = 0.25, \, \sigma = 0.3$. So,for finde percentage I should to use such formulas: $$ \mathbf{P}(|\xi - a|< \delta) = 2\Phi\left( \frac{\delta}{\sigma} \right) . $$
So $$ \mathbf{P}(|\xi - a|< \delta) = 2\Phi\left( \frac{0.25}{0.3} \right) = 0.5934. $$
But correct answer is $\approx 1.24\%$. I do not quite understand how such an answer was received in principle. I hesitate a little at this moment, do you have any ideas where I was wrong?