C955: Applied Probability and Statistics

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Feeling shaky before C955: Applied Probability and Statistics test? Feel strong with our practice questions.

Free C955: Applied Probability and Statistics Questions

1.

The link between interest rates and the quantity of new house starts in an area is being examined by an economist.
What category should this study fall under?

  • Quantitative->categorical

  • Categorical->quantitative

  • Quantitative->quantitative

  • Categorical->categorical

Explanation

Explanation:

Interest rates are numerical values, making them a quantitative variable. The number of new housing starts is also a countable numeric value, which is quantitative. Since both variables are numeric, this study examines a quantitative-to-quantitative relationship.

Correct Answer:

Quantitative->quantitative


2.

Review the linear inequality y > -⁵/₃x + 1.
Which graph corresponds to this inequality?

Explanation

Explanation:

y > -⁵/₃x + 1.

When we replace the greater than sign with equal sign;

y = -⁵/₃x + 1.

From the resulting equations show a y intercept of 1. Hence the line cuts the y axis at 1. This helps us eliminate all the options where the line does not cut the y axis at 1. Since the line in all the options is the same, we eliminate all the options with a straight line since our equality says greater than hence the options in the line won’t satisfy our  linear inequality. 

Testing the two remaining options.

Testing the graph shaded on the top right side. 

Picking point (2, 0); 

y > -⁵/₃x + 1.

0 > ( -⁵/₃*2) + 1

0 > -7/₃

Since 0 is greater than -7/3 this graph correctly represents the linear inequality.

Correct answer


3.

A study is done to find out the relationship between the consumption of pizza and the number of accidents over the years. For this, a researcher conducted a study on the sale of pizza and the number of accidents and found them to be highly correlated. What is the possible lurking variable in this study?

  • Population

  • No lurking variable exists in the study.

  • Pizza consumption

  • The number of accidents

Explanation

Correct answer

a. Population

Explanation

The correct answer is option a, Population, because a lurking variable is an external variable not directly studied but potentially influencing both the independent and dependent variables. Here, population size could be the lurking variable since a larger population could naturally lead to increased pizza consumption (due to higher food demands) and also to more accidents (due to increased traffic or activities). Population growth could cause an artificial correlation between pizza consumption and accidents without any direct causal link.


4.

What is the value of the expression below?

½ + ⅓ + ⅙

  • ³/₅

  • ¹/₅

  • ³/₆

  • 1

Explanation

Explanation:

We need to add the fractions ½, ⅓, and ⅙.

The least common denominator (LCD) of 2, 3, and 6 is 6.

Convert each fraction to have a denominator of 6:

½ = ³/₆

⅓ = ²/₆

⅙ = ¹/₆

Now add them together:

³/₆ + ²/₆ + ¹/₆ = ⁶/₆ = 1

Correct Answer:

D. 1


5.

Describe the significance of the probability calculated for a student who knows 7 answers and guesses on the remaining questions.

  • The probability shows that guessing is always detrimental to performance.

  • The probability reflects the total number of questions answered correctly regardless of knowledge.

  • The probability indicates the likelihood of achieving a certain level of success despite guessing, highlighting the impact of knowledge on performance

  • The probability is irrelevant to the number of questions known

Explanation

Explanation:

The probability in this context quantifies the chance that a student achieves a particular number of correct answers, given they know some answers and guess on the rest. It demonstrates how prior knowledge influences the likelihood of success and how guessing affects performance outcomes. This allows educators or students to assess expected performance considering both knowledge and chance.

Correct Answer:

The probability indicates the likelihood of achieving a certain level of success despite guessing, highlighting the impact of knowledge on performance.


6.

A study investigates the effect of study hours on exam scores among college students.
Which statement describes the relationship between study hours and exam scores?

  • Study hours are the explanatory variable, while exam scores are the response variable.

  • Both study hours and exam scores are explanatory variables.

  • Both study hours and exam scores are response variables.

  • Exam scores are the explanatory variable, while study hours are the response variable.

Explanation

Explanation:

In this study, the goal is to examine how study hours influence exam scores. Study hours are the independent variable (explanatory variable) because they are manipulated or measured to see their effect. Exam scores are the dependent variable (response variable) because they respond to changes in study hours.

Correct Answer:

Study hours are the explanatory variable, while exam scores are the response variable.


7.

A recipe calls for 312 tablespoons of water. This is twice the amount of milk needed.
How much milk is needed for the recipe?

  • 112 tablespoons

  • 114 tablespoons

  • 134

  • 1 tablespoon

Explanation

Explanation

The recipe uses 3 12 tablespoons of water, which is twice the amount of milk. To find the milk amount, divide the water amount by 2:

312 ÷ 2 =72 ÷ 2=74=134 tablespoons   

Correct Answer

C. 134 tablespoons


8.

What is the correct line graph for y = 6 - 2x
 

Explanation

Solution:

The equation y = 6 - 2x

Re-writing the equation: y = -2x + 6. 

The y intercept for this line is 6. Hence all the lines that do not close y-intercept at 6 will be incorrect. The correct option is d since this line passes the y-axis at 6.


9.

A bank teller commutes to and from work each day and is interested in the relationship between the time it takes to get to work in the morning and the time it takes to return home at the end of the day. The bank teller determines the following:
The equation of the least squares regression line is ( y = 5.2 + 1.15x )
( x ) is the time (in minutes) to drive to work in the morning
( y ) is the time (in minutes) to drive home in the evening
The correlation coefficient is ( r = 0.75 )
On one particular morning, it takes the bank teller 50 minutes to drive to work.
How long does the model predict it will take to drive home?

  • 37.5 minutes

  • 38.96 minutes

  • 57.5 minutes

  • 62.7 minutes

Explanation

Explanation

Use the regression equation to predict ( y ):

( y = 5.2 + 1.15x )

Substitute ( x = 50 ):

( y = 5.2 + 1.15(50) = 5.2 + 57.5 = 62.7 ) minutes

Correct Answer

D. 62.7 minutes


10.

If a spinner has four equal regions (red, blue, green, yellow), what is the probability of getting the same color on two consecutive spins?

  • 1/5

  • 1/3

  • 1/4

  • 1/2

Explanation

Explanation:

For the first spin, any color can appear. To get the same color on the second spin, the probability must match the first spin's outcome. With four equal regions, the chance of matching is 1 out of 4 for the second spin. Therefore, the probability of getting the same color on two consecutive spins is 1/4.

Correct Answer:

1/4


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