KYOTE Statistics and Probability 2 — Questions and Answers
Question 1: A student's four test scores are 80, 85, 90, and 75. What score is needed on the fifth test to bring the average to 85?
- 90
- 95 (Correct answer)
- 100
- 85
Correct answer: 95
A mean of 85 over 5 tests requires a total of 425; since 80+85+90+75=330, the fifth score must be 425−330=95.
Question 2: Two cards are drawn without replacement from a standard 52-card deck. What is the probability that both cards are aces?
- 1/221 (Correct answer)
- 1/169
- 1/52
- 4/52
Correct answer: 1/221
The probability is (4/52) × (3/51) = 12/2652 = 1/221.
Question 3: In a box-and-whisker plot, which feature represents the median?
- The left whisker
- The right whisker
- The line inside the box (Correct answer)
- The right edge of the box
Correct answer: The line inside the box
The line drawn inside the box of a box-and-whisker plot always represents the median (Q2) of the data.
Question 4: A scatter plot shows a strong positive correlation between study time and test scores. What does this mean?
- As study time increases, test scores decrease
- As study time increases, test scores also tend to increase (Correct answer)
- Study time and test scores have no relationship
- Both variables decrease at the same rate
Correct answer: As study time increases, test scores also tend to increase
A positive correlation means that as one variable increases, the other tends to increase as well.
Question 5: Which measure of central tendency is most affected by extreme outlier values?
- Mode
- Median
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean uses every value in its calculation, so an extreme outlier pulls it significantly up or down.
Question 6: How many ways can 4 students be selected and arranged in a line from a group of 6 students?
- 24
- 360 (Correct answer)
- 720
- 15
Correct answer: 360
This is a permutation: 6 × 5 × 4 × 3 = 360 ordered arrangements.
Question 7: A coin is flipped 3 times. What is the probability of getting exactly 2 heads?
- 1/4
- 3/8 (Correct answer)
- 1/2
- 1/8
Correct answer: 3/8
There are 3 favorable outcomes (HHT, HTH, THH) out of 8 total outcomes, giving a probability of 3/8.
KYOTE Statistics and Probability 2
A student's four test scores are 80, 85, 90, and 75.
What score is needed on the fifth test to bring the average to 85?