-12 points DevoreSto:95.E. D41 My N Let be the number of packages being mailed b

Question

-12 points DevoreSto:95.E. D41 My N Let be the number of packages being mailed by a random ly selected customer at a certain shipping racility. Suppose the distribution, of Xis as follows. p(x) 0.4 0.1 0.2 0.3 (a) Consider a random sample of size -2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of x. 1.5 2.5 3 3.5 P(x) (b Refer to part (a) and calculate PX s 2.5) (c) Again consider a random sample of size n - 2, but now facus 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 outoome and use the probabilities from part (a). PTR) (d) If a random sample of size -4 is selected, what is P 1.5)? [Hint: You should not have to list all possible outcomes, only those for which x s 15 Need Help? ReadITalk to a Tutor

Explanation / Answer

a)

b)

P(xbar < = 2.5) = 0.16+0.08+0.17+0.28

=   0.69

c)

x1 x2 P(x1) P(X2) P(x1)*P(X2) sample mean 1 1 0.4 0.4 0.16 1 2 1 0.1 0.4 0.04 1.5 3 1 0.2 0.4 0.08 2 4 1 0.3 0.4 0.12 2.5 1 2 0.4 0.1 0.04 1.5 2 2 0.1 0.1 0.01 2 3 2 0.2 0.1 0.02 2.5 4 2 0.3 0.1 0.03 3 1 3 0.4 0.2 0.08 2 2 3 0.1 0.2 0.02 2.5 3 3 0.2 0.2 0.04 3 4 3 0.3 0.2 0.06 3.5 1 4 0.4 0.3 0.12 2.5 2 4 0.1 0.3 0.03 3 3 4 0.2 0.3 0.06 3.5 4 4 0.3 0.3 0.09 4

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