Let X Be the Number of Packages Being Mailed by a Randomly

question 9

Essay

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: $$\begin{array} { c c c c c } \hline x & 1 & 2 & 3 & 4 \\\hline p ( x ) & .4 & .3 & .2 & .1 \\\hline\end{array}$$
a. Consider a random sample of size n = 2 (two customers), and let $\bar { X }$
be the sample mean number of packages shipped. Obtain the probability distribution of $\bar { X }$
.
b. Refer to part (a) and calculate $P ( \bar { X } \leq 2.5 )$
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 $P ( \bar { X } \leq 1.5 )$
? (Hint: You should not have to list all possible outcomes, only those for which $\bar { x } \leq 1.5 . )$

---

Definitions:

Relational Immediacy

A concept in communication that refers to the closeness or personalness achieved between participants in communication, enhancing openness and reducing perceived distance.

Interactional Behavior

Refers to how individuals act and react in the presence of others, encompassing verbal and non-verbal communication.

Quantitative Evaluation

The process of using numerical data to measure and assess outcomes or characteristics.

Self-expression

The act of conveying or manifesting one’s thoughts, feelings, or creativity through various forms, such as speech, art, or behavior.