Please solve (a), (b), and (c) only! (a) is not all 1/7 (b) is not 0.2, 0.6, or 0.4285.(c) is not 0.25, 0.375, 0.25, and 0.125Thank you! **Image Transcription for Educational Website:**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:\[\begin{array}{c|ccccc}x & 1 & 2 & 3 & 4 \\\hlinep(x) & 0.2 & 0.3 & 0.4 & 0.1 \\\end{array}\]**(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 $\bar{X}$.\[\begin{array}{c|cccccc}\bar{X} & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 \\\hlineP(\bar{X}) & & & & & & & \\\end{array}\]**(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).]\[\begin{array}{c|cccc}R & 0 & 1 & 2 & 3 \\\hlineP(R) & & & & \\\end{array}\]**(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 $\bar{X} \leq 1.5$.]---*Note:* The table headers for $\bar{X}$ and $R$ indicate different possible outcomes. The probability distributions $P(\bar{X})$ and $P(R)$ need to be calculated based on

Name: Please solve (a), (b), and (c) only! (a) is not all 1/7 (b) is not 0.2
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Description: Please solve (a), (b), and (c) only! (a) is not all 1/7 (b) is not 0.2, 0.6, or 0.4285.(c) is not 0.25, 0.375, 0.25, and 0.125Thank you! **Image Transcription for Educational Website:**Let $X$ be the number of packages being mailed by a randomly se

Given: x 1 2 3 4 P (X) 0.2 0.3 0.4 0.1

Math

Probability

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. 1 2 3 4 P(x) 0.2 0.3 0.4 0.1 (a) Consider a random sample of size n = 2 (two customers), and let x be the sample mean number of packages shipped. Obtain the probability distribution of x. 1 1.5 2 2.5 3 3.5 4 (b) Refer to part (a) and calculate P(X S 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).] 1 2 P(R)

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. 1 2 3 4 P(x) 0.2 0.3 0.4 0.1 (a) Consider a random sample of size n = 2 (two customers), and let x be the sample mean number of packages shipped. Obtain the probability distribution of x. 1 1.5 2 2.5 3 3.5 4 (b) Refer to part (a) and calculate P(X S 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).] 1 2 P(R)

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

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Please solve (a), (b), and (c) only!

(a) is not all 1/7

(b) is not 0.2, 0.6, or 0.4285.

Thank you!

**Image Transcription for Educational Website:**

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:

\[
\begin{array}{c|ccccc}
x & 1 & 2 & 3 & 4 \\
\hline
p(x) & 0.2 & 0.3 & 0.4 & 0.1 \\
\end{array}
\]

**(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 $\bar{X}$.

\[
\begin{array}{c|cccccc}
\bar{X} & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 \\
\hline
P(\bar{X}) & & & & & & & \\
\end{array}
\]

**(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).]

\[
\begin{array}{c|cccc}
R & 0 & 1 & 2 & 3 \\
\hline
P(R) & & & & \\
\end{array}
\]

**(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 $\bar{X} \leq 1.5$.]

---

*Note:* The table headers for $\bar{X}$ and $R$ indicate different possible outcomes. The probability distributions $P(\bar{X})$ and $P(R)$ need to be calculated based on

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