The probability of finding an O2 molecule in a sample of oxygen at 300 K with a speed between 500 m/s and 510 m/s can be approximated by the area of a rectangle under the Maxwell-Boltzmann distribution curve, using the average speed of 505 m/s for the height of the rectangle.
The probability that an O2 molecule in a sample of oxygen at 300 K has a speed between 500 m/s and 510 m/s can be estimated using the Maxwell-Boltzmann distribution. The area under the curve within the range of interest represents the probability of finding molecules with speeds within that range. Since the speeds 500 m/s and 510 m/s are close to each other, we can approximate the area under the curve by calculating the area of a small rectangle, where the width is the difference in speeds (510 m/s - 500 m/s) and the height is the value of the probability density function at a speed that is representative of this interval, such as the midpoint at 505 m/s.