Question 1:
A corporation produces packages of paper clips. The number of clips per package varies, as indicated below for a sample of 20 packages.
|
53
|
47
|
51
|
52
|
47
|
49
|
51
|
50
|
48
|
53
|
52
|
50
|
51
|
48
|
52
|
47
|
47
|
52
|
50
|
51
|
Create a probability density function.
What is the probability that a randomly chosen package contains between 47 and 52 clips (inclusive) per package?
Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Question 2:
Let X be a discrete random variable. If Pr(X<5) = 1/4, and Pr(X>5) = 1/6, then what is Pr(X=5)?
Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Question 3:
Let X be a discrete random variable. If Pr(X<9) = 3/8, and Pr(X<=9) = 7/16, then what is Pr(X=9)?
Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Question 4:
A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table.
|
Number of complaints
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Probability
|
0.20
|
0.25
|
0.26
|
0.14
|
0.10
|
0.05
|
Question 5:
What is the probability of between 1 and 2 (inclusive) complaints received per week?
Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
Question 6:
A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table.
|
Number of complaints
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Probability
|
0.17
|
0.30
|
0.33
|
0.07
|
0.05
|
0.08
|
What is the mean of complaints received per week?
Please round your answer to the nearest hundredth.
Question 7:
A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table.
|
Number of complaints
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Probability
|
0.15
|
0.20
|
0.41
|
0.11
|
0.06
|
0.07
|
What is the standard deviation of complaints received per week?