We measure the viscosity of a particular fluid by putting th…
We measure the viscosity of a particular fluid by putting the fluid in a calibrated tube, and then dropping a small ball into the tube. X is the random variable which denotes how many seconds it takes for the ball to drop to the bottom of the tube. The longer the drop, the more viscous the fluid. Below is a histogram of your latest 15 trials. MidTerm_QuestionL_Chart_A.png Your team wants to consider those 15 trials to be one batch, and notes that the average dropping time is 1.38 seconds for the batch shown. It also assumes the standard deviation for the population of all dropped balls through this tube with this fluid is assumed to be 1.25 seconds. Your company is advertising the average dropping time as 2 seconds, and this is assumed to be the population average. For this product, more viscous (longer dropping times) is better. Your team member says, “Hey, I think we can use the Central Limit Theorem here even though this histogram doesn’t even look remotely normally distributed. Let’s take 3 more batches, so we will have a total of 4 batches of 15 ball drops. That’s 60 balls total. Then the distribution of the sample means for batch 1, batch 2, batch 3, and batch 4 will be normally distributed, with a mean and standard deviation we can measure. That will tell us what we really want to know: if our product really does have a mean of 2 and a stdev of 1.25, what are the chances that a random sample like the one we took will give those results?” Is your team member correct? If so, apply the Central Limit Theorem and tell me the results. If not, tell me why not and what, if any, changes could be made to get the information the team wants. (Note: this is specifically a question on the Central Limit Theorem, not on hypothesis testing. Please don’t formulate or test any hypotheses here. Just discuss the Central Limit Theorem.)