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 0.1 0.4 0.3 (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. 4 1 1.5 2 2.5 3 3.5 P(X) 0.04 0.04 0.17 0.2 0.22 .24 0.09 (b) Refer to part (a) and calculate P(X ≤ 2.5). 0.45 (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 P(R) 0.3 1 0.36 2 3 0.22 0.12 (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.] 0.0045
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 0.1 0.4 0.3 (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. 4 1 1.5 2 2.5 3 3.5 P(X) 0.04 0.04 0.17 0.2 0.22 .24 0.09 (b) Refer to part (a) and calculate P(X ≤ 2.5). 0.45 (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 P(R) 0.3 1 0.36 2 3 0.22 0.12 (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.] 0.0045
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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.
X
1 2
3 4
p(x) 0.2 0.1
0.4 0.3
(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
P(X) 0.04
0.04
0.17
2
2.5
3
3.5
0.2
0.22
.24
0.09
4
(b) Refer to part (a) and calculate P(X ≤ 2.5).
0.45
=
(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) 0.3
0.36
0.22
0.12
(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.]
0.0045
×](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd08e19be-7e5e-4944-9492-2c1f0e254c97%2F0df2a597-bd94-4270-bd21-51ad8263cb2b%2Fmh5gr2t_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.
X
1 2
3 4
p(x) 0.2 0.1
0.4 0.3
(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
P(X) 0.04
0.04
0.17
2
2.5
3
3.5
0.2
0.22
.24
0.09
4
(b) Refer to part (a) and calculate P(X ≤ 2.5).
0.45
=
(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) 0.3
0.36
0.22
0.12
(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.]
0.0045
×
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