Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows: x 1 2 3 4 p ( x ) 0.4 0.3 0.2 0.1 a. Consider...

Let
X
be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows:

a. Consider a random sample of size n= 2 (two customers), and let x̄be the sample mean a number of packages shipped. Obtain the probability distribution of x̄.

b. Refer topart (a) and calculate P( x̄
≤
2.5).

c. Again consider a random sample of size n= 2,but now focus on the statistic
R
= the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of
R
.

[

Hint
Calculate the value of
R
for each outcome and use the probabilities from part (a).)

d. If a random sample of size n= 4 is selected, what is P( x̄≤ 1.5)?
[

Hint
You should not have to list all possible outcomes, only those for which x̄
≤ 1.5.)