C955: Applied Probability and Statistics
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Free C955: Applied Probability and Statistics Questions
If x = 15, evaluate the following expression:
x · (x − 7)
-
8
-
105
-
120
-
225
Explanation
Explanation:
We substitute x = 15 into the expression x · (x − 7).
x · (x − 7) = 15 · (15 − 7)
= 15 · 8
= 120
Correct Answer:
C. 120
There are 14 black, 16 white, and 10 red balls in a box. What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?
- 7/200
- 7/100
- 21/200
- 50/Jul
Explanation
Explanation
Correct answer: (A) 7/200
Total balls = 14 + 16 + 10 = 40
With replacement, probabilities stay the same each draw:
- P(black) = 14/40 = 7/20
- P(red) = 10/40 = 1/4
- P(white) = 16/40 = 2/5
Multiply:
(7/20) × (1/4) × (2/5) = 14 / 400 = 7 / 200
A die with faces numbered 1 to 3 is rolled twice. The sample space is represented in the following table:
What is the probability of rolling a double (both numbers the same)?
Explanation
Explanation:
The doubles are (1,1), (2,2), and (3,3). There are 3 doubles out of 9 total possible outcomes.
P(double) = =
Correct Answer:
Review the following inequality:
y ≤ −4x + 1
Which shaded region is described by this inequality?
Explanation
Explanation
y ≤ −4x + 1
y = -4x + 1
From the equation the y intercept is 1 hence option 2 and 3 are eliminated as they have -1 as the y intercept.
Testing the two remaining graphs to see which fits the inequality.
Testing point 0,0 on the first option,
y ≤ −4x + 1
0 ≤ (−4 * 0) + 1
0 ≤ 1
Since this is true the option is correct.
Correct Option
A university conducts a survey among faculty and students to determine support for a new campus recycling initiative.
The results of the survey are shown in the following 2 × 2 contingency table:
|
Support |
Oppose |
Total |
|
|
Faculty |
40 |
10 |
50 |
|
Students |
200 |
300 |
500 |
-
20%
-
60%
-
80%
-
40%
Explanation
Explanation:
To find the percent of students who oppose the initiative, divide the number of students who oppose (300) by the total number of students surveyed (500) and multiply by 100:
(300 ÷ 500) × 100 = 60%
Correct Answer:
60%
A researcher has collected information on participants at a marathon and wants to display the ages of the runners:
16, 25, 36, 27, 48, 35, 26, 57, 45, 35, 66, 47, 28, 34, 25, 48
Which graph type should be used to display these data?
-
Bar graph
-
Stem-and-leaf plot
-
Line graph
-
Pie chart
Explanation
Correct answer
b. Stem-and-leaf plot
Explanation
The correct answer is option b, Stem-and-leaf plot, because it effectively organizes numerical data by displaying both distribution and individual data values. It clearly shows the frequency of ages while preserving original numerical data. A stem-and-leaf plot is ideal for relatively small datasets, allowing a clear visual representation of the spread and central tendency of the data.
If y = −2, evaluate the following expression:
(10 − y) · (1 + y)
-
-12
-
-6
-
4
-
6
Explanation
Explanation
Substitute y = −2 into the expression:
(10 − (−2)) · (1 + (−2)) = (10 + 2) · (1 − 2) = 12 · (−1) = −12
Correct Answer
A. −12
What is the product of 0.6 and 0.25?
-
0.15
-
0.18
-
0.20
-
0.22
Explanation
Explanation
To find the product, multiply the two decimals: (0.6 * 0.25). First ignore the decimals and multiply 6 × 25 = 150. Then place the decimal point. Since 0.6 has one decimal place and 0.25 has two decimal places, the product must have three decimal places. Therefore, 150 becomes 0.150, which is the same as 0.15.
Correct answer
A. 0.15
An investigation is being conducted to assess the impact of sleep duration on cognitive performance in teenagers.
Which statement describes the relationship between sleep duration and cognitive performance?
-
Cognitive performance is the explanatory variable, while sleep duration is the response variable
-
Sleep duration is the explanatory variable, while cognitive performance is the response variable
-
Both sleep duration and cognitive performance are explanatory variables
-
Both sleep duration and cognitive performance are response variables
Explanation
Explanation
The explanatory variable (independent variable) is the factor that is manipulated or observed to see its effect on another variable. Here, sleep duration affects cognitive performance, so sleep duration is the explanatory variable, and cognitive performance is the response variable.
Correct Answer
B. Sleep duration is the explanatory variable, while cognitive performance is the response variable
Describe how to find the probability of a random variable uniformly distributed between two values
-
You use the mean of the distribution to find the probability
-
You multiply the probabilities of each outcome together.
-
To find the probability, calculate the length of the interval of interest and divide it by the total length of the distribution interval.
-
You sum the probabilities of each individual outcome
Explanation
Explanation:
For a uniform distribution, every outcome within the range is equally likely. The probability of the variable falling within a specific interval is proportional to the length of that interval. Therefore, the probability is calculated by dividing the length of the interval of interest by the total length of the distribution interval.
Correct Answer:
To find the probability, calculate the length of the interval of interest and divide it by the total length of the distribution interval.
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