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) 0.2 0.4 0.3 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 3 4 X P(X) 0.04 0.16 0.28 X .46 2.5 .28✔✔✔ .17 (b) Refer to part (a) and calculate P(X ≤ 2.5). .76 (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).] R 0 1 2 3 P(R) 28 2 3.5 ✓ .06 ✔ .01 .04 (d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which X < 1.5.]
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) 0.2 0.4 0.3 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 3 4 X P(X) 0.04 0.16 0.28 X .46 2.5 .28✔✔✔ .17 (b) Refer to part (a) and calculate P(X ≤ 2.5). .76 (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).] R 0 1 2 3 P(R) 28 2 3.5 ✓ .06 ✔ .01 .04 (d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which X < 1.5.]
A First Course in Probability (10th Edition)
10th Edition
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...
Related questions
Question
![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 0.4 0.3 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
3
4
X
P(x) 0.04
.76
(b) Refer to part (a) and calculate P(X ≤ 2.5).
0.16
R
P(R) 28
0.28
X .46
2.5
.2
.28
.17
(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).]
0
1
2
3
.04
3.5
.06✔
.01
✓
(d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which X < 1.5.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96ac55a0-db6b-49b8-93c5-a355a6dbc337%2F559fe2eb-30d5-45c4-8e3e-062f7f76c967%2Fuatf8im_processed.png&w=3840&q=75)
Transcribed Image Text: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 0.4 0.3 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
3
4
X
P(x) 0.04
.76
(b) Refer to part (a) and calculate P(X ≤ 2.5).
0.16
R
P(R) 28
0.28
X .46
2.5
.2
.28
.17
(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).]
0
1
2
3
.04
3.5
.06✔
.01
✓
(d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which X < 1.5.]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON