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# Statistics Problem Set: Coffee or Tea?

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1. Poll of 200 people was conducted to analyze if liking Tea or Coffee is related to gender.
Here are results of this poll:
Tea Coffee
Male 10 70
Female 40 80

a) Based on these data, what is the probability that a person likes Coffee if the person is a Male?

b) Based on these data, what is the probability that person likes Tea if Female?

1. What number is missing in this discrete probability distribution?
x P(x)
0 0.40
1
2 0.20
3 0.10

3. For the given discrete probability distribution calculate probability that x will be less than 3 (3 is not included)
x P(x)
0 0.26
1 0.33
2 0.21
3 0.10
4 0.08
5 0.02

4. For the given Discrete Distribution, calculate Expected Value.
x P(x)
0 0.1
1 0.2
2 0.3
3 0.4

5. You flip the coin 7 times. Apply Binomial Distribution to calculate probability that Head will happen exactly 3 times.

6. Sixty percent of the students at a particular community college are female. If 12 students at that community college are selected at random, find the probability that 5 will be female.

7. Network has in average 5 computers failure per week. Apply Poisson distribution to find probability that it will be only one computers failure per week.

8. Find the Median for the following set of data: 25, 20, 8, 10, 28, 16, 22, 15

9. For Normal distribution with mean 50 and standard deviation 10 find probability that x will be below 35.

10. A company's three departments are Office, Sales and Production. The table below shows how many people work in each department by gender.
Office Sales Production
Male 4 6 13
Female 8 2 7

Based on this table find probability that randomly selected person in this company is Female OR works in the Office department.

11. Calculate expressions with factorials: 6!/4!

12. Normal Distribution has mean 200 and standard deviation 40. Convert x = 220 to z-value.

13. Use Standard Normal Distribution to find probability P(z < 0.5). Apply Appendix Table C or Excel function NORMSDIST(z).

14. Use Standard Normal Distribution to find probability P(z > 2). Remember: Appendix Table C and Excel function Normsdist(z) give you P(z < 2). Use formula: P(z>2) = 1 - P(z<2)

15. The weights of professional baseball players follow a normal distribution with a mean of 200 pounds and a standard deviation of 25 pounds. Find the probability that a randomly selected professional baseball
player has a weight less than 225 pounds.

16. 200 people were asked if they watch NBC News. Only 16 said "yes". Based on this sample data, estimate population proportion with confidence level 95% (zc=1.960).

17. Sample with n = 36 has mean = 20 with a standard deviation 6. Estimate population mean with confidence level 90% (zc=1.645). Round the answer up to the whole numbers.

18. Find Quartiles Q1, Q2 and Q3 for the following data collection:
48, 32, 23, 14, 24, 45, 50, 42, 56, 90, 66, 71, 68, 70

19. Create frequency distribution table for the following set of numbers:
15, 21, 22, 24, 25, 31, 33, 34, 35, 36, 38, 38, 40, 43, 45, 50

20. Number of students who graduate College every year is Normal Distribution with mean = 400 and standard deviation 50. Find probability that this year between 300 and 500 students will graduate College.

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#### Solution Preview

1. There are 10+70=80 males, among these males, there are 70 of them who like coffee.
Therefore, the probability=70/80.

2. There are 40+80=120 females, among these females, there are 40 of them who like tea.
Therefore, the probability: 40/120.

3. Since the summation should be equal to 1, the missing probability: 1-0.40-0.20-0.10=0.30.

4. P(x<3)=0.26+0.33+0.21=0.80

5. Expected value=0*0.1+1*0.2+2*0.3+3*0.4=2.

6. ...

#### Solution Summary

The solution analyzes if tea or coffee is related to gender.

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