Question
An internet pharmacy advertises that it will deliver the over-the-counter products that customers purchase in 3...
- An internet pharmacy advertises that it will deliver the over-the-counter products that customers purchase in 3 to 6 days. The manager of the company wanted to be more precise in its advertising. Accordingly, she recorded the number of days it took to deliver to customers. From the data, the following probability distribution was developed.
Assume that X is a random variable. X will denote the number of days to deliver the product(s).
|
x |
P(x) |
|
0 |
0 |
|
1 |
0 |
|
2 |
.01 |
|
3 |
.04 |
|
4 |
.28 |
|
5 |
.42 |
|
6 |
.21 |
|
7 |
.02 |
|
8 |
.02 |
- Derive the cumulative distribution function manually in Excel.
|
x |
P(X ≤ x) |
|
0 |
|
|
1 |
|
|
2 |
|
|
3 |
|
|
4 |
|
|
5 |
|
|
6 |
|
|
7 |
|
|
8 |
b. What is the expected number of days for a delivery? Calculate the expected value.
c. Calculate the variance of the probability distribution and standard deviation?
Homework Answers
Answer #1
b.
Expected value =(ΣXi)/N
=36/9
=4 days
c.
Variance ={ [(ΣXi)^2]/n} -[ΣXi/n]^2
=(204/9) - (4)^2
=22.6667 - 16
=6.6667
Standard deviation = (var)^1/2
=(6.6667)^1/2
=2.582
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