Let X be the number of packages being mailed by a randomlyselected customer at a certain shipping facility. Suppose thedistribution of X is as follows: x 1 2 3 4 p(x) .4 .3 .2 .1
a. Consider a random sample of size n = 2 (two customers), andlet X be the sample mean number of packages shipped. Obtain theprobability distribution of X .
b. Refer to part (a) and calculate P (Xbar is less than or equalto 2.5)
c. Again consider a random sample of size n = 2, but now focuson the statistic R = the sample range (difference between thelargest and smallest values in the sample). Obtain the distributionof R.
d. If a random sample of size n = 4 is selected, what is p (Xbarless than or equal to 1.5)?
