Confidence Intervals · Challenge problem

A lab measures a quantity whose readings are normally distributed with unknown mean $\mu$. The lab believes the standard deviation is $\sigma = 10$ and always reports $\bar x \pm 1.96\cdot\dfrac{10}{\sqrt n}$ as its "$95\%$" interval for $\mu$. In fact the true standard deviation is $15$. What is the actual probability that such an interval contains $\mu$? Give your answer to four decimal places.