Hi,

The question 5 asks “What is the probability of an engine having these two measurements? ( temperature of 17.5 and a vibration of 48)”.

The probability of such a measurement is in fact zero, because the question is asking about a point measurement. The area below a point size data is zero.

The area below the whole bell curve adds up to 1 (the integral is 1). To find a probability of a measurement you have to give a range, like: What is the probability of the temperature being between 16 and 17 and vibration between 47.5 and 48.5, for example. Then you can integrate the curve inside this range for each feature, multiply them, and get the combined probability.

The confusion arises because the graph y axis is labeled P(x) (probability of x) but it is in fact a probability density of x (P(x) per measurement unit). You have to integrate this curve to get the probability, you can’t just read the y axis value to get the probability.