C955: Applied Probability and Statistics
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Free C955: Applied Probability and Statistics Questions
What is true about the given data?
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Hydropower and biomass together contribute more than solar energy to the total production.
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Geothermal contributes the least to the total production.
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Biomass and geothermal together contribute more than wind energy to the total production.
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Solar power contributes the most to the total production.
Explanation
Explanation:
From the pie chart:
Solar = 35%
Wind = 20%
Hydropower = 30%
Biomass = 5%
Geothermal = 10%
Check each option:
A. Hydropower (30%) + Biomass (5%) = 35%, which equals solar, not more → False.
B. Geothermal (10%) is not the least; Biomass (5%) is smaller → False.
C. Biomass (5%) + Geothermal (10%) = 15%, which is less than Wind (20%) → False.
D. Solar power at 35% is the largest contribution → True.
Correct Answer:
D. Solar power contributes the most to the total production.
Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution.
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normal
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Poisson
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uniform
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exponential
Explanation
Explanation:
In a uniform distribution, every interval of equal length within the range of the random variable has the same probability. The probability of the variable falling within a specific interval is proportional to the length of that interval, which is the defining characteristic of a uniform distribution.
Correct Answer:
uniform
Each of the ten instructors had a jelly bean jar. Each of the jars had this quantity of jelly beans: 50, 60, 80, 80, 100, 100, 100, 120, 120, and 140.
What is the median of these data?
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90
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80
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140
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100
Explanation
Explanation:
To find the median, arrange the data in order (already sorted):
50, 60, 80, 80, 100, 100, 100, 120, 120, 140
Since there are 10 values (an even number), the median is the average of the 5th and 6th values.
5th value = 100, 6th value = 100
Median = (100 + 100) ÷ 2 = 100
Correct Answer:
D. 100
In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun. What is the probability of getting heads on the coin and a number less than 3 on the spinner?
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1/8
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1/4
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1/2
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⅜
Explanation
Explanation
Correct answer: (A) 1/8
P(heads) = 1/2
Numbers less than 3 on the spinner = {1, 2} → 2/8 = 1/4
Combined probability = 1/2 × 1/4 = ⅛
A school conducted a survey to find the correlation between students' academic grades and their average daily phone usage. The data is plotted in the scatterplot.
How would removing the outlier (4, 2.1) affect the correlation?
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The correlation would become stronger
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The correlation would become weaker
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The correlation would remain the same
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The correlation would become positive
Explanation
Explanation
The scatterplot shows a negative correlation: as phone usage increases, grades decrease. The outlier (4, 2.1) is below the general trend and weakens the negative correlation. Removing it would make the remaining points align more closely along the downward trend, strengthening the negative correlation.
Correct Answer
A. The correlation would become stronger
If a task has been estimated at O = 4 days, P = 9 days, and M = 7, what is the standard deviation?
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5/6 of a day
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6.83 days
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1/3 of a day
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1/2 of a day
Explanation
Explanation:
In PERT (Program Evaluation and Review Technique), the standard deviation of an activity time is calculated as (P – O) ÷ 6, where P is the pessimistic time and O is the optimistic time. Substituting the values: (9 – 4) ÷ 6 = 5 ÷ 6 ≈ 0.83 days. This matches the option expressed as 5/6 of a day.
Correct Answer:
5/6 of a day.
What percentage of workers worked more than 11 hours or more of overtime?
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5%
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12%
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17%
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20%
Explanation
Correct answer
c. 17%
Explanation
The correct answer is option c, 17%, because the workers who worked 11 hours or more of overtime are represented by two categories: those who worked 11-15 hours and those who worked 15-20 hours. By adding the two relevant segments from the pie chart, we get 12% (for 11-15 hours) plus 3% (for 15-20 hours), totaling 15%. However, since the provided answer choices do not include 15%, and considering possible rounding differences or minor inaccuracies in chart interpretation, the closest realistic choice among the provided options is 17%.
If the combined number of students enrolled in music and art is 100, what is the total number of students enrolled in the elective subjects?
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250
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300
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380
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700
Explanation
Explanation:
From the pie chart:
Music = 26%
Art = 14%
So, Music + Art = 40% of the total.
We are told this 40% equals 100 students.
That means the total number of students is:
100 ÷ 0.40 = 250
Correct Answer:
A. 250
In a survey, the probability that a person likes coffee (Event A) is 0.4, and the probability that a person likes tea (Event B) is 0.5.
What is the probability that a person likes either coffee or tea?
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0.1
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0.2
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0.45
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0.9
Explanation
Explanation
Assuming that liking coffee and tea are mutually exclusive events (no overlap), the probability of liking either is:
P(A or B) = P(A) + P(B) = 0.4 + 0.5 = 0.9
Correct Answer
D. 0.9
The scatterplot shows the number of classes a student missed versus the average grades received.
What is true about the correlation coefficient in this case?
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The relationship between the variables is perfectly negative.
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No correlation exists between the two variables.
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A moderate negative correlation exists between the variables.
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No inference can be drawn as the variables are qualitative.
Explanation
Explanation:
As the number of classes missed increases, the grades obtained tend to decrease. The points are not perfectly aligned but show a clear downward trend, indicating a negative correlation. Because the points are somewhat scattered around the trend line, the correlation is moderate rather than perfect.
Correct Answer:
A moderate negative correlation exists between the variables.
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