Confidence Intervals · Superchallenge problem

A normal population has known $\sigma$. From a sample of 24 values a 95% interval $\bar x_1 \pm 1.96\,\sigma/\sqrt{24}$ is built for the mean. Then a NEW independent sample of 25 values is taken. What is the probability that the new sample mean $\bar x_2$ falls inside the first interval? Round to three decimal places.