A population consists of N = 5 numbers: 1, 3, 5, 6, and 7. It can be shown that the mean and standard deviation for this population are µ = 4.4 and σ = 2.15, respectively.
a. Construct a probability histogram for this population.
b. Use the random number table, Table 10 in Appendix I, to select a random sample of size n = 10 with replacement from the population. Calculate the sample mean, . Repeat this procedure, calculating the sample mean for your second sample.
c. To simulate the sampling distribution of , we have selected 50 more samples of size n = 10 with replacement, and have calculated the corresponding sample means. Construct a relative frequency histogram for these 50 values of . What is the shape of this distribution?
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