Probability
thrilzRaun
284questions.pdf
Good luck to:
Answer the following questions based on the dataset seen below.
{𝟐, 𝟑, 𝟓, 𝟕, 𝟏𝟏}
1. Calculate the sample mean.
a. 5.6
b. 28
c. 3.5777
d. 3.2
e. 5
2. Calculate the sample
median. a. 5.6
b. 28
c. 3.5777
d. 3.2
e. 5
3. Calculate the sample
variance. a. 3.57
b. 3.2
c. 12.7999
d. 10.24
e. Not enough information to calculate
4. What is 𝑥1? a. 1
b. 2
c. 3
d. 28
e. 208
5. What is ∑ 𝑥𝑖? a. 5.6
b. 28
c. 208
d. 5
6. Calculate the mode. a. 2, 3, 5, 7 , 11
b. No mode
7. Let’s say that 𝑠2 = 9. What is the sample variance? a. 3
b. 9
c. 81
d. 243
8. Let’s say someone does not want to wait every ten years for the census to come out. Consequently, this person starts going from door to door in “Neighborhood X” because they
want to figure out what the composition of Iowa City is like. What group is the sample? a. Neighborhood X
b. Iowa City
9. Let’s say that I conducted a survey of the clas to determine how much money a student at
University of Iowa spends on average getting ready for the first football game of the season.
Let’s say the class average was $27.43. Would it be reasonable to conclude that the population
average is guaranteed to be $27.43?
a. Yes, the sample average is definitely the same as the population average
b. No, the sample average is an approximation of the population average
The following questions (9 through 11 )are about possible errors. Tell whether each situation is possible to be correct or not correct.
10. Let’s pretend that a student listed 𝑛 = 1,000 as a parameter. Is it possible the student has done this correctly?
a. Correct
b. Wrong
11. Let’s pretend that a statistics student calculates �̅� = −17. Is it possible the student has done this correctly?
a. Correct
b. Wrong
12. Let’s pretend that a statistics student calculates the following cumulative frequency table:
Is it possible the student calculated the above cumulative frequency table correctly? a. Correct
b. Wrong
13. Where is the mode on the following graph? Assume that the y-axis is frequency.
A B C D
The following questions (14 and 15) are about “categorical” or “quantitative” variables. Select whether
each situation is a categorical variable or a quantitative variable.
14. Recording the average amount of coffee each student consumes measured in ounces. a. Categorical
b. Quantitative
15. Recording the amount of coffee each student consumes as “small,” “medium,” or “large.”
a. Categorical
b. Quantitative
Use the CUMULATIVE frequency table below to answer the following questions about the die rolls.
16. How many times was a 4 rolled? a. 2
b. 6
c. 7
d. 13
e. 24
17. How many times was a number less than 9 rolled?
a. 46
b. 64
c. 71
d. 8
e. 56
18. How many times was a number between 6 and 9 (NOT inclusive) rolled?
a. 47
b. 31
c. 40
d. 23
e. 10
Answering the following questions about summation notation. When necessary, use the data shown
below:
𝑛
19. ∑ 𝑖=1
𝑥𝑖
𝑛 = 2 with 𝑥1 = 2 and 𝑥2 = 4
a. 6
b. 10
c. 13
20. ∑𝑛 (𝑥𝑖 − �̅�) 𝑖=1
a. 0
b. 3
c. 6
d. 4
e. 2
Answer the following difficult question from Unit 1.
21. The mean statistics grade for a class of 24 students is 84. When one of the students drops the class, the new mean is 87. What was the grade of the student that dropped the class?
a. 15
b. 37
c. 81
d. 90
e. Not enough information to calculate
22. In a group of 20 scores, the largest score is increased by 60 points. What would happen to the
mean? a. It will remain the same
b. It will increase by 3
c. It will increase by 10
d. It will increase by 60
e. There is not enough information to answer the question
23. In a group of 20 scores, the largest score is increased by 60 points. What would happen to the
median? a. It will remain the same
b. It will increase by 3
c. It will increase by 10
d. It will increase by 60
e. There is not enough information to answer the question
Match the corresponding r value with the following scatter plots.
24. 24. a. -1
b. 0.05
c. -0.4
d. 0.90
25. 25.
a. -1
b. 0.05
c. -0.4
d. 0.90
26. 26.
a. -1
b. 0.05
c. -0.4
d. 0.90
27. 27.
a. -1
b. 0.05
c. -0.4
d. 0.90
Do the following residual plots satisfy the assumption necessary for linear regression?
28. 28. a. Yes (Good)
b. No (Bad)
Use the chart below to answer questions about correlation and causation.
Math Doctorates Awarded vs. Suicides by Hanging, Strangulation, and Suffocation
29. Math doctorates cause suicide. a. True
b. False
30. Math doctorates and suicide are positively correlated.
a. True
b. False
31. Mat doctorates and suicide are negatively correlated.
a. True
b. False
Use the chart below to answer the following questions. Assume the regression equation is as follows:
�̂� = 𝟎. 𝟗𝟕𝒙 + 𝟏. 𝟗𝟎
32. If 𝑥 = 2, what is the actual value?
a. 5
b. 3.84
c. -3.84
d. 0.10
e. -0.10
33. If 𝑥 = 2, what is the predicted value? a. 5
b. 3.84
c. -3.84
d. 0.10
e. -0.10
34. Is the residual positive or negative when 𝑥 = 2? a. Positive
b. Negative
Answer the following questions based on the story below.
Let’s pretend you want to graph the regression equation for the relationship between height and
weight. After doing so, you get the following equation: 𝑊 ̂ 𝑒𝑖𝑔ℎ𝑡 = 2.41 ∗ 𝐻𝑒𝑖𝑔ℎ𝑡 − 3.7. For this
problem, weight is measured in pounds and height is measured in inches.
35. Explain the meaning of the slope in this context. a. Every inch, weight goes up by 2.41 pounds
b. Every inch, weight goes down by 2.41 pounds
c. Every inch, weight goes down by 3.7 pounds
d. Every inch, weight goes up by 3.7 pounds
36. Would the correlation coefficient be positive or negative?
a. Positive
b. Negative
c. Neither
d. Not enough information to tell
37. Taylor Swift is 5’10” (70 inches tall) and weighs 114 pounds. Would this be a negative residual or
a positive residual?
a. Positive
b. Negative
c. Neither
d. Not enough information to tell
Answer the following questions about the statistic shown below:
“Liebrecht’s Number” is a new statistic that involves ordering all the values in a data set and then adding
the distances from one number to the next. An example of how it is calculated can be shown below when
𝑛 = 3.
𝐿𝑖𝑒𝑏𝑟𝑒𝑐ℎ𝑡′𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 = (𝑥3 − 𝑥2) + (𝑥2 − 𝑥1)
38. Use the data set {10, 13, 15} to calculate “Liebrecht’s Number.” a. 2
b. 3
c. 5
d. 10
39. Assuming the data is ordered from lowest to highest, what does “Liebrecht’s Number” help
measure?
a. Central Tendency (middle)
b. Dispersion (spread)
Use the following information to answer the next few questions.
Let’s say Alex and Brian go play darts. Alex will throw one dart and Brian will throw one dart. The
probability Alex hits the target is 0.7. The probability that Brian hits the target is 0.5. The probability the
target gets hit is 0.9.
40. What is the probability that Alex AND Brian hit the target? a. 0.1
b. 0.2
c. 0.3
d. 0.4
41. What is the probability that the target is NOT hit? a. 0.1
b. 0.2
c. 0.3
d. 0.4
42. What is the probability that ONLY Alex hits the target? a. 0.1
b. 0.2
c. 0.3
d. 0.4
Answer the next few questions.
43. If you flip a fair coin followed by rolling a 6-sided die, what is the probability of getting heads followed by rolling a 5 or 6?
a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6
Answer the following questions about a traffic light.
Let’s pretend that Alex’s drive home has three traffic lights on the drive and assume each traffic light is
independent. Let’s say that the probability of driving through a green traffic light is 0.6.
44. When driving through 3 traffic lights, what is the probability of getting no green lights? a. 0.064
b. 0.216
c. 0.6
d. 0.784
e. 0.936
45. What is the probability of getting AT LEAST one green light when driving through three traffic lights?
a. 0.064
b. 0.216
c. 0.6
d. 0.784
e. 0.936
46. Let’s say that Alex is having some amazing luck and has already driven through 2 green traffic
lights. Now that Alex has successfully driven through 2 green traffic lights in a row so far, what is
the probability that the 3rd traffic light is green? (Hint: Remember that the traffic lights are independent)
a. 0.064
b. 0.216
c. 0.6
d. 0.784
e. 0.936
Use the following chart to answer the next two questions.
47. What is the probability of randomly selecting an individual that has a C in the class? a. 5/23
b. 9/46
c. 7/46
d. 1/46
48. What is the probability of selecting someone that has a C in the class AND studied 2-6 hours a
week?
a. 9/46
b. 7/46
c. 2/46
d. 1/46
49. What is the probability of selecting someone that has a C in the class GIVEN they studied 2-6 hours a week?
a. 1/7
b. 1/6
c. 1/5
d. 1/4
50. What is the probability of selecting someone that studied 2-6 hours a week GIVEN they have a C in the class?
a. 1/7
b. 1/6
c. 1/5
d. 1/4
