in an enormous number of random phenomena, the distribution functions of such sums are approximately normal. Some examples are the weight of a man, the height ofa woman, the error made in a measurement, the position and velocity ofa molecule of a gas, the quantity ofdiffused material, the growth distribution of plants, animals, or their organs, and so on. The weight of a man, for example, is the result ofa large number of environmental and genetic factors which are more or less unrelated but each of which contributes only a small amount to the weight. I. Sampling Distributions: To get an idea of what is going on when you are talking about a sampling distribution, consider a population of 5 test scores from a small class. The test scores are {133, 95, 90, 35, 30}. Let us obtain samples of size 2 from this population with replacement. In other words, after you select the rst test score, you put it back for selection again. Sampling with replacement from a small population is similar to sampling from a large population. 1. List all 25 possible samples. For example, [30,33] and [30,35] are two of the 25 samples possible. Note that i am writing the selected scores in parentheses separated by a comma. 2. Now, give each of the 25 x bars associated with the samples above. 3. Now compute the mean of the sample means. In other words, what is mu sub it her? 4. What is the mean of the population? 5. What is the standard deviation of the sample means from [2] above? You should use Microsoft Excel to answer this question. Please remember to calculate the population standard deviation since the 25 x bars represents all of our sample means. 6. What is the population standard deviation of the original population? Use Excel to calculate this as well