A tunnel of length 170 m will be drilled from two sides. From experience we know that what is managed in different days can be understood as a stochastic variable with expected value 5.0 meters and standard deviation 1.2 meters.
Find out with a suitable approximation the probability that the tunnel takes more than 18 days to be completed.
I know the CLT and what it means but I get confused with the fact that we are supposed to calculate days and we are given meters.
Let's call $X_i$ the distance drilled by team $X$ on day $i$, and $Y_i$ the distance drilled by team $Y$
You need to find the probability that:
$$\sum_{i=1}^{18} (X_i+Y_i) < 170$$
Now you can make your approximations ( first, $X_i \sim Y_i$ and the random variables are independant and identically distribued), so it's
$$\sum_{i=1}^{36} X_i < 170$$
Then you can use a normal approximation for this sum