We have given population data for a variable. For each exercise, do the following tasks.
a. Find the mean, $\mu,$ of the variable.
b. For each of the possible sample sizes, construct a table similar to Table 7.2 on page 299 and draw a dotplot for the sampling distribution of the sample mean similar to Fig. 7.1 on page 299 c. Construct a graph similar to Fig. 7.3 and interpret your results.
d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.
e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most $0.5 .$
Population data: 1,2,3,4,5,6.