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February Regional
Statistics Team: Question #1
If 𝑋̅ = 35.2, 𝑌̅ = 42.4, 𝑆𝑥 = 5.3, 𝑆𝑦 = 3.2, 𝑎𝑛𝑑 𝑟 2 = .96 for negatively correlated data
sets X and Y.
Let:
A= Slope of the least-square regression line (Round to two decimal places)
B= Y-intercept of the least-square regression line (Round to two decimal places)
C= X-intercept of the least-square regression line (Round to two decimal places)
D= Residual for the data point (3,62) (Round to two decimal places)
𝐴+𝐵
What is 𝐶+𝐷? (Round to two decimal places)
February Regional
Statistics Team: Question #2
Given the data set:
{3, 1, 4, 1, 2, 7, 18, 28, 71, 18, 17, 88, 31, 41, 59, 26, 54, 4, 6, 43, 34, 46, 57, 60, 26, 65, 72, 38, 41}
Let:
A= Sum of the mean and median of the data set (Round to two decimal places)
B= Number of outliers found using the IQR method
C= Sum of IQR and Range
D= Standard deviation if the set was considered a sample minus variance if the set
was considered a population. (Use exact values and round to two decimal places at
the end)
What is A+B+C+D? (Round to two decimal places)
February Regional
Statistics Team: Question #3
Given:
𝜇𝑋 = 2; 𝜇𝑌 = 5; 𝑆𝑋 = 3; 𝑆𝑌2 = 16 and X and Y are independent.
Let:
A= 𝜇𝑋+𝑌
B= 𝜇7𝑥−7𝑌
C= 𝑆3𝑋−2𝑌
What is A-B+C? (Round to two decimal places)
February Regional
Statistics Team: Question #4
Consider a distribution x that is a normal distribution with a mean of 10 and
standard deviation of 4. Calculate all probabilities using the empirical rule.
Let:
A= 𝑃(6 < 𝑋 < 14)
B= 𝑃(2 < 𝑋)
C= 𝑃(𝑋 < 22)
D= 𝑃(6 < 𝑋 < 18)
What is A+B+CD? (Rounded to 2 decimal places)
February Regional
Statistics Team: Question #5
Suppose you are rolling a six-sided dice that is weighted based on the number of
dots on the face of the side. (The probability of rolling a 2 is twice as likely as a 1, the
probability of rolling a 6 is three times as likely as a 2, …) You roll this dice 20 times
and count the number of times you roll a 3.
Let:
A= Mean number of 3s you roll
B= Variance of the number of 3s you roll
C= Probability it takes more than five rolls to roll your first 3 (Round to three
decimal places)
D= Probability you roll five 3s (Round to three decimal places)
What is the mean of the data set (A,B,C,D)? (Round to two decimal places)
February Regional
Statistics Team: Question #6
The results of the Pre and Post test for nine students are summarized below.
Conduct a test to see if there is a significant increase in performance after
instruction.
Pre
Post
1
56
58
2
88
89
3
47
55
4
79
85
5
83
76
6
75
84
7
72
75
8
54
62
9
92
95
Let:
A= Value of the test statistic, rounded to two decimal places
B= P-value of the test, rounded to 3 decimal places
C= Standard deviation of the test statistic, rounded to two decimal places
D= 2 if the data is significant at a 5% significant level, 1 if the data is NOT significant
at a 5% significance level
What is 𝐴𝐵 + 𝐶 𝐷 ? (Round to three decimal places)
February Regional
Statistics Team: Question #7
Given a standard deck of playing cards
Let:
A= Probability you randomly draw a club and then a heart without replacement
B= Probability you randomly draw a spade or king
C= Probability you draw five cards without replacement and draw at least one ace.
What is AB+C? (Round to three decimal places)
February Regional
Statistics Team: Question #8
The results of a Calculus test have mean of 75 and standard deviation of 12. Suppose
the teacher wants to transform the results to have a mean of 85 and standard
deviation of 10.
Let:
A= Slope of the transformation equation
B= Y-intercept of the transformation equation
C= If Brad scored a 63 on the test originally, what is his transformed score?
D= If Angela has a transformed score of 95, what was her original score?
What is AB+(D-C)?
February Regional
Statistics Team: Question #9
In a certain country, 5% of the population has a disease. The test for the disease
results in a false positive 28.5% of the time. The test results in a positive identity
97% of the time, if the person has the disease.
Let:
A= Probability a patient with the disease tests negative
B= Probability a randomly selected patient tests positive
C= Probability that the patient does not have the disease, given that the patient
tested positive
D= Probability of an incorrect reading
What is the slope of the line connecting the points (A,B) and (C,D)? (Round to three
decimal places)
February Regional
Statistics Team: Question #10
Consider the following probability distributions:
Distribution 1
Test 1 Score 3
Proportion .1
1
a
4
2b
7
.3
5
.3
7
2a
1
b
8
2b
6
.25
Distribution 2
Test 2 Score 2
Proportion a
Let:
A= Value of a
B= Value of b
C= Mean of Distribution 1
D= Standard Deviation of Distribution 2 (rounded to two decimal places)
What is 𝐴10𝐵 + 𝐶 − 𝐷? (Round to three decimal places)
February Regional
Statistics Team: Question #11
Given the following set of data
Gender/Division
Male (M)
Female (F)
Let:
A= P(F)
B= 𝑃(𝑀 ∪ 𝐴)
C= 𝑃(𝐹 ′ ∩ 𝑇)
D= 𝑃(𝐴′ |𝑀)
𝐴
What is 𝐵 + 𝐶 + 𝐷?
Theta (T)
12
17
Alpha (A)
10
24
Mu
22
15
February Regional
Statistics Team: Question #12
Consider the following statements:
Geometric and Binomial trials have identical conditions.
The area under a normal curve is approximately one.
Correlation is a non-resistant measurement.
The square of the range of possible values of the correlation coefficient is 1
The range of a data set is always greater than the IQR
All outliers are influential points.
The range of percentile values is [0,100).
An increase in sample size will increase the probability of correctly failing to reject a
true null hypothesis.
Stratified sampling is a form of a simple random sample.
How many of the above statements are false?
February Regional
Statistics Team: Question #13
If Jeff scored a 75 on a test that had a distribution of (70,5), George scored a 20 on a
test that had a distribution of (15,2), Bob scored a 100 on a test that had a
distribution of (80,15), and Karl scored a 50 on a test that had a distribution of
(45,3). Rank the students in order of who did the best relative to other students
taking the same test, starting with the person who did the best. (Distribution of (x,y)
means a normal distribution with a mean of x and standard deviation of y.)
February Regional
Statistics Team: Question #14
Suppose you are rolling a fair six sided dice ten times and observing the number of
time you roll a five.
Let:
A= Mean of the situation
B= Standard deviation of the situation (Round to two decimal places)
C= Probability you roll a five, 5 times (Round to three decimal places)
D= Probability you roll at least two fives (Round to three decimal places)
What is A+B+C+D? (Round to two decimal places)