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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. 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.]

Calculus For The Life Sciences
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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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 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.]
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.]
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