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 4 2 3 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. 2 X 1 1.5 P(x) 0.04 0.04 0.12 (b) Refer to part (a) and calculate P(X ≤ 2.5). 2.5 3 3.5 4 × 0.04 × 0.16 × .15 × 0.09 the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of (c) Again consider a random sample of size n = 2, but now focus on the statistic R = R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).] R P(R) 2 3 (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 4 2 3 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. 2 X 1 1.5 P(x) 0.04 0.04 0.12 (b) Refer to part (a) and calculate P(X ≤ 2.5). 2.5 3 3.5 4 × 0.04 × 0.16 × .15 × 0.09 the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of (c) Again consider a random sample of size n = 2, but now focus on the statistic R = R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).] R P(R) 2 3 (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

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

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