Number of times the car ran out of petrol. (More detail given)?

Question

A car ride uses a mean of 7 litres of petrol with a standard deviation of 0.5 litres. Assuming that the amount of petrol used is normally distributed.

i) If the car usually has only 8 litres in its tank, how many times in next 1000 rides will the car ran out of petrol?

Answer 1

This depends on how exact your answer needs to be. You can use the 68-95-99.7 rule to determine that in the 95% of the time you will fall within two standard deviations (i.e., bet. 6 and 8). Half of the remaining 5% is usage below 6 liters, so only 2.5% of the time do you run out of gas.

To be more exact, you can look up the z-score given by:
(X - mu) / (sigma) = (8 - 7) / .5 = 2 and find that the result is that you run out of gas 2.2275% of the time.

If you need more explanation, just add that to your additional details. Good luck!

Answer 2

The tank of the car has 8 litres of tank
Each car ride uses a mean of 7 litres ( with SD of 0.5 litres)
In 1000 rides, it would use a mean of 7000 litres
So frequency of it running out of petrol = 7000 / 8 = 875

So your answer is 875 times

Answer 3

It's a pretty small tank, my car has a 50 litre tank. I would carry a spare can of petrol with you at all times and thewn you will never run out.