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 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 x̄ be the sample mean a number of packages shipped. Obtain the probability distribution of x̄. b. Refer topart (a) and calculate P( x̄ ≤ 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( x̄≤ 1.5)? [ Hint You should not have to list all possible outcomes, only those for which x̄ ≤ 1.5.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 |
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 x̄ be the sample mean a number of packages shipped. Obtain the
b. Refer topart (a) and calculate P( x̄ ≤ 2.5).
c. Again consider a random sample of size n= 2,but now focus on the statistic R = the sample
d. If a random sample of size n= 4 is selected, what is P( x̄≤ 1.5)? [ Hint You should not have to list all possible outcomes, only those for which x̄ ≤ 1.5.)
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