Question 1

A sample of 7 law students recorded the number of hours spent studying the course material during the week before the final exam. The data is: 5, 5, 6, 6, 7, 6, 7. What is the median number of hours studied?

Accepted Answer

$$6$$

Question 2

Given the data set: 5, 5, 6, 6, 7, 6, 7, calculate the interquartile range (IQR).

Accepted Answer

$$1$$

Question 3

A world-wide fast food chain wants to assess the influence of income on number of visits to their restaurants. A sample of households was asked about the number of times they visit a fast food restaurant (X) during last month as well as their monthly income (Y). The correlation coefficient $$r$$ was found to be $$0.775. $$What does this value indicate?

Accepted Answer

There is a strong positive association between income and number of visits.

Question 4

Consider the frequency distribution: 
Class: 14-19, Frequency: 4; 20-24, Frequency: 6; 25-29, Frequency: 10. What is the cumulative frequency for the class 25-29?

Accepted Answer

$$20$$

Question 5

For the frequency distribution above, what is the probability that a randomly selected observation has a value at least 15?

Accepted Answer

$$0.4$$

Question 6

A management consulting company surveys personnel and finds that 82% of analysts have an MBA degree or are over age 35. 40% of those who do not have an MBA are age 35 or less. What is the probability that a randomly selected analyst who does not have an MBA is age 35 or less?

Accepted Answer

$$0.4$$

Question 7

If three analysts are randomly selected (without replacement) who have an MBA degree, what is the probability that all of them are age 35 or less, given that 69% of MBA holders are age 35 or less?

Accepted Answer

$$0.329$$

Question 8

Given the joint probability table:
MBA Degree & Over 35: $$0.22$$; MBA Degree & At most 35: $$0.28$$; No Degree & Over 35: $$0.15$$; No Degree & At most 35: $$0.12. $$What is the marginal probability that an analyst is over 35?

Accepted Answer

$$0.37$$

Question 9

Let the distribution function for $$X be $$given by $$P(X=x) = c(x^3$ + 4x^2$ + 5x + 3)$$ for $$x = 1, 2, 3, 4, 5. $$What is the value of $$c$$ that makes this a probability distribution function?

Accepted Answer

$$\frac{1}{170}$$

Question 10

The Ministry of Foreign Affairs receives job applications from graduates of Bilkent University. The probability distribution of the random variable $$X ($$number of Bilkent graduates recruited) is: $$P(X=0)=0.64$$, $$P(X=1)=0.32$$, $$P(X=2)=0.04. $$What is the expected value $$E(X)$$?

Accepted Answer

$$0.4$$

Question 11

Using the same probability distribution for $$X$$ above, what is the variance $$Var(X)$$?

Accepted Answer

$$0.32$$

Question 12

Suppose a fast food chain wants to test the association between income and number of visits to their restaurants. If the sample correlation coefficient is $$r = 0.775$$, what is the coefficient of determination?

Accepted Answer

$$0.601$$

Question 13

Given the data set: 5, 5, 6, 6, 7, 6, 7, what is the value of the lower inner fence for outliers using the formula $$Q_1 - 1.5$$ 	imes IQR$$?

Accepted Answer

$$5$$

Question 14

A company finds that 82% of analysts either have an MBA degree or are over age 35. If 70% of analysts have an MBA degree, what is the probability that an analyst is over age 35?

Accepted Answer

$$0.12$$

Question 15

If $$P(MBA) = 0.7$$ and $$P(Over\ 35) = 0.37$$, what is $$P(MBA \cap Over\ 35)$$ given $$P(MBA \cup Over\ 35) = 0.82$$?

Accepted Answer

$$0.25$$

Question 16

Given the joint probability table, what is the probability that an analyst is at most 35 years old and does not have an MBA degree?

Accepted Answer

$$0.12$$

Question 17

If $$P(MBA | At\ most\ 35) = 0.69$$ and $$P(At\ most\ 35) = 0.6$$, what is $$P(MBA \cap At\ most\ 35)$$?

Accepted Answer

$$0.414$$

Question 18

Suppose the probability that a randomly selected analyst has an MBA degree given that he or she is at most 35 years old is $$0.69. $$What is the probability that a randomly selected analyst is at most 35 years old and has an MBA degree?

Accepted Answer

$$0.414$$

Question 19

Given the probability distribution $$P(X=0)=0.64$$, $$P(X=1)=0.32$$, $$P(X=2)=0.04$$, what is the probability that at least one Bilkent graduate is recruited?

Accepted Answer

$$0.36$$

Statistics Exam Questions and Solutions: Data Description, Probability, and Distributions

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