Let X be the number of packages being mailed by a randomly selected customer at

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. px) 0.4 0.2 0.1 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. 2.5 3.5 P(x) 0.16 0.16 0.12 0.28 0.13 0.06 0.0 (b) Refer to part (a) and calculate PX s 2.5) 0.72 (c) Again consider a random sample of size n2, but now focus on the statistic Rthe 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).] P(R) (d) If a random sample of size n-4 is selected, what is PXs 1.5)? [Hint: You should not have to list all possible outcomes, only those for which x s 1.5.]

Explanation / Answer

c) frin above P(R) =P(X1)*P(X2)

therefore

d)

P(Xbar<=1.5) =P(all four are 1+3 are 1 and 4th is 2+3 are 1 and 4 th is 3+2 are 1 and other are 2 are 2)

=0.44+4*(0.4)3*0.2+4*(0.4)3*0.1+6*(0.4)3*(0.2)2=0.1408

R 0 1 2 3 P( R) 0.3 0.26 0.2 0.24

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