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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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
p(x) 0.4 0.1 0.2 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
2
2.5
3
3.5
4
P(x)0.16
0.08
0.17
0.1
0.12
0.28
0.09
(b) Refer to part (a) and calculate P(X s 2.5).
0.69
(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
1
2
3
P(R) ||0.3
|x
(d) If a random sample of sizen = 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.]
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 p(x) 0.4 0.1 0.2 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 2 2.5 3 3.5 4 P(x)0.16 0.08 0.17 0.1 0.12 0.28 0.09 (b) Refer to part (a) and calculate P(X s 2.5). 0.69 (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 1 2 3 P(R) ||0.3 |x (d) If a random sample of sizen = 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.]
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