ASk Your Teach Let X be the number of packages being mailed by a randomly select
ID: 3061252 • Letter: A
Question
ASk Your Teach 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. p(x) 0.1 0.2 0.3 0.4 (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 1.5 2.5 3.5 4 P(x) (b) Refer to part (a) and calculate P(X s 2.5) 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).] (c) 0 2 PR) 4 is selected, what is Rx 1.5)? [Hint: You should not have to list all possible outcomes, If a random sample of size n only those for which (d) 15]Explanation / Answer
a)
here for P(Xbar) =P(X1)*P(X2)
from above:
b)
P(Xbar<=2.5) =0.35
c)
from above:
d)
P(Xbar<=1.5) =P(all sample are 1 +1 is 2 and other 3 are 1+1 is 3 and other 3 are 1+2 is 2 and other 2 are 1)
=0.14+4*0.13*0.2+4*0.13*0.3+6*0.12*0.22=0.0045
x 1 1.5 2 2.5 3 3.5 4 P( xbar) 0.01 0.04 0.1 0.2 0.25 0.24 0.16