Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of Xis as follows: x 1 2 3 4 p(x) 0.4 0.3 0.2 0.1 a. Consider a random sample of size n = 2 (two customers), and let x̅ be the sample mean number of packages shipped. Obtain the probability distribution of x̅ . b. Refer topart (a) and calculate P( x̅ ≤2.5). 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).) d. If a random sample of size n = 4 is selected, what is P( x̅ ≤1.5)? [ Hint. You should not have to list all possible outcomes, only those for which x̅ ≤ 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 Xis as follows:
|
x |
1 |
2 |
3 |
4 |
|
p(x) |
0.4 |
0.3 |
0.2 |
0.1 |
a. Consider a random sample of size n = 2 (two customers), and let x̅ be the sample mean number of packages shipped. Obtain the
b. Refer topart (a) and calculate P( x̅ ≤2.5).
c. Again consider a random sample of size n= 2, but now focus on the statistic R = the sample
[ Hint. Calculate the value of R for each outcome and use the probabilities from part (a).)
d. If a random sample of size n = 4 is selected, what is P( x̅ ≤1.5)?
[ Hint. You should not have to list all possible outcomes, only those for which x̅ ≤ 1.5.)
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