Normal Distribution Question

Hi, could someone please explain what to do for part (c)? I don't really know where to start. Initially, I thought it was the probability that the journey takes less than 165 miles, given it takes less than 119 which I think is correct. But surely if the probability is 90%, then we know the journey must be 119 miles? I just can't get my head around it. Could someone please explain? Thanks.

Working backwards a bit
P(x<165 | x>119) = PIx<165 & x>119) / P(x>119) ...
which gives the numbers / picture in the solution though the right tail is a lot smaller than the left, hence why the conditional (answer) is close to 1. From b) you know that
P(x>119) = 0.9
so journeys > 119 miles have a cumulative probability of 0.9. 119 miles (or 120 to the nearest mile) is where the cumulative splits as 0.1 and 0.9.

Thank you that does help. But in the question it says that Mark does have a 90% chance of completing a journey on a single full tank of petrol, so surely this must mean that his journey is going to be 119 miles and then he will stop? So how could he travel 165 miles?

The probability of his journey being exactly 119 miles using a normal distribution is zero (ignoring the fact that there is a bit of rounding going on). Youre dealing with cumulative probabilities, so x lies in an interval and as above
P(x>119) = 0.9
So a 90% chance of completing the journey corresponds to the interval x>119.