Problem 1

	In our work on suspensions of particles in 
fluids, many properties depend on the diameter of the 
particles (e.g., migration rate, wall effects, etc.).  It thus 
becomes a tedious but necessary task to measure the 
diameter of these micron sized particles.  The 
technique we use is video microscopy, in which we 
couple a microscope objective to a video camera and 
take digital images of the particles.  The particle images 
are then displayed on a screen and the size of the 
spheres are either determined through image 
processing algorithms, or directly with a cursor, 
depending on the image clarity.  The information we 
want to get is the mean size of the particles, and also 
the population standard deviation (a measure of the 
width of the size distribution).  In this problem we will 
examine this process.

a.  A student has measured the following particle 
diameters using a video microscope (measurements 
are in microns):

	51.1
	52.9
	54.2
	52.3
	46.7
	49.0
	54.3
	54.1
	49.1
	53.9

Calculate the mean and an unbiased estimate of the 
population standard deviation.

b. Assuming only random scatter, provide a 95% 
confidence interval for the true population mean.

c. How many measurements are required to reduce the 
width of this confidence interval to less than +-1% of 
the mean size?

d. If the calibration of the videomicroscope itself is 
only good to about +- 2%, about how many particle 
measurements should the student make?