Please see description box and attached file for questions.

Questions 1-15 are worth 3 points each for a total of 45 points.

 

  1. (3 points) Which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for salaries of college professors.  (Circle one)

 

A.   Ordinal

B.    Ratio

C.    Nominal

D.   Interval

 

 

  1. (3 points) If a tax auditor selects every 10,000th tax return that is submitted, which form of sampling is he/she using?  (Circle one)

 

A.   Convenience

B.    Stratified

C.    Random

D.   Systematic

E.    Cluster

 

 

  1. (3 points) ___________________ are sample values that lie very far away from the vast majority of other sample values.

 

 

  1. (3 points) TRUE  /  FALSE :  The mathematical formula for finding  is .  (Circle one) 

 

 

  1. (3 points) A __________ is a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data).  (Circle one)

 

 

A.   Histogram

B.    Scatter Plot

C.    Dotplot

D.   Pie Chart

 

 

  1. (3 points) The ___________________ of a data set is a measure of center indicating the value that occurs with the greatest frequency.

 

 

  1. (3 points) TRUE  /  FALSE :  Quartiles are measures of location which divide a data set into 100 groups with about 1% of the values in each group.  (Circle one)

 

 

  1. (3 points) TRUE  /  FALSE :  For any event A, the probability of A is between -1 and 1 inclusive.  That is, .         

 

 

  1. (3 points) For any event , it’s ___________________, denoted by , consists of all outcomes in which event  does not occur.

 

  1. (3 points) Two events A and B are __________ if they cannot occur at the same time (that is, their Venn diagrams do not overlap).  (Circle one)

 

A.   Disjoint

B.    Mutually Exclusive

C.    Compound

D.   All of the Above

E.    A & B Only 

 

 

  1. (3 points) The ___________________ of B given A, dented by , represents the probability of event B occurring after it is assumed that event A has already occurred.

 

 

  1. (3 points) A(n) ____________________ is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure.  (Circle one)

 

A.   Probability Distribution

B.    Random Variable

C.    Probability Histogram

D.   Expected Value

 

 

  1. (3 points) Which of the following is nota requirement of a binomial probability distribution?  (Circle one)

 

A.   The procedure has a random number of trials. 

B.    The trials must be independent.

C.    Each trial must have all outcomes classified into two categories (e.g. success and failure).

D.   The probability of a success remains constant in all trials.

E.    All of the above are requirements of the binomial probability distribution.

 

 

  1. (3 points) The ___________________ is a discrete probability distribution that applies to occurrences of some event over a specified interval.  The random variable x is the number of occurrences of the event in an interval.

 

 

  1. (3 points) The probability that event A occurs in a first trial and event B occurs in a second trial is denoted as:         (Circle one) 

 

A.   P(A and B)

B.    P(A ∩B)

C.    P(A) * P(B | A)

D.   All of the above

E.    A & B only

 

NOTE: For the following questions, you can use Excel (the data files are available on LEO). 

 

16.   (70 points) The data set consists of the heights (in inches) of 20 randomly selected women.  Use this data set to complete the tasks below. 

 

67

61

65

62

65

75

61

67

64

60

66

59

70

64

67

68

62

65

63

71

 

16.A.     (20 points)   Construct a Frequency Distribution (including the Relative Frequency) of the data using 5 classes.  Explain your selection of class width.  

NOTE: If you use Excel to solve the problem, indicate that you have done so (e.g. “See Solution 11.A on Excel Solution File”); however, you still need to fill in the table below.

 

 

Lower Class Limit

Upper Class Limit

Frequency

Relative Frequency

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Class Width =

 

16.B.     (5 points)   Draw a Histogram of the data set using the Frequency Distribution data you’re your solution to 11.A.  

NOTE: You can say “See Solution 11.B on Excel Solution File” (assuming you use Excel to create the histogram). 

 

16.C.     (4 points)  What is the arithmetic mean of the data set?

 

16.D.     (10 points) Use the Frequency Distribution found in 11.A to estimate the mean (NOTE: this will not necessarily be the same solution as in 11.C).

 

16.E.      (3 points)  What is the median of the data set?

 

16.F.      (3 points)  What is the mode of the data set?  Note, if there is more than one mode, list all of them.

 

16.G.     (6 points)  What is the standard deviation of the data set?

 

16.H.     (3 points)  What is the variance of the data set?

 

16.I.       (5 points)  Draw a box-plot graph of the data set.  Label each part of the graph.

 

16.J.       (6 points)  Draw a Stem Plot (or Stem-and-Leaf Plot) of the data set.

 

16.K.     (5 points)  Is a woman who is 72 inches tall considered “unusual”?  Why or why not?

 

 

  1. (25 points)  Body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20˚F and a standard deviation of 0.62˚F. 

 

17.A.     (5 points) Using the empirical rule, what temperature range accounts for 68% of healthy adults?

 

17.B.      (5 points) Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures between 96.34˚F and 100.06˚F?

 

17.C.     (5 points) Using Chebyshev’s theorem, what temperature range accounts for 75% of healthy adults?

 

17.D.      (5 points) Using Chebyshev’s theorem, what percentage of healthy adults fall within 96.34˚F and 100.06˚F?

 

17.E.       (5 points) When would we use Chebyshev’s theorem instead of the empirical rule?

 

 

  1. (20 points)  Consider the following scenario.  A bag contains 4 Red marbles, 3 Blue marbles, and 7 Green marbles. 

 

18.A.     (5 points)  If an event is defined as “I randomly choose ONE marble from the bag,” what is the probability that I choose a Blue marble?

 

18.B.     (5 points) If an event is defined as “I randomly choose ONE marble from the bag,” what is the probability that I do NOT choose a Red marble?

 

18.C.     (5 points)  If an event is defined as “I randomly choose TWO marbles from the bag WITHOUT replacement,” what is the complete sample space for the outcome of this event?  NOTE: You can abbreviate the colors as R, B, G for Red, Blue, and Green, respectively.

 

18.D.      (5 points)  If an event is defined as “I randomly choose TWO marbles from the bag WITHOUT replacement,” what is the probability of choosing two Red marbles? 

 

  1. (15 points) The table below describes the smoking habits of a group of asthma suffers.

 

 

Nonsmoker

Occasional smoker

Regular smoker

Heavy smoker

Men

374

36

86

36

Women

380

37

60

32

 

19.A.     (5 points) Given that an asthma sufferer is an occasional smoker, what is the probability that the person is a woman?

 

19.B.     (5 points) Given that an asthma sufferer is a man, what is the probability that the person is a regular smoker?

 

19.C.     (5 points)  Given that an asthma sufferer is a regular smoker, what is the probability that the person is a nonsmoker?

 

 

  1. (10 points) Counting Problems

 

20.A.     (5 points) 8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

 

20.B.     (5 points) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

 

  1. (30 points) The data set below details a random variable x is the number of houses sold by a realtor in a single month at the Strano Real Estate office.  Show your work to receive partial credit

 

Houses Sold (x)       

Probability P(x)       

0

0.24

1

0.01

2

0.12

3

0.16

4

0.01

5

0.14

6

0.11

7

0.21

 

21.A.     (15 points) Given the data set above, determine if it is a valid probability distribution. If it is not valid, explain why.  If it is, find the mean and variance of the given probability distribution.

 

21.B.     (5 points) What is the expected value for this probability distribution?  Note: if the distribution is not a valid probability distribution, you can respond “Not Applicable.”

 

21.C.     (5 points) What is the probability that the realtor will sell 5 or more houses in one month.

 

21.D.     (5 points) Would it be considered “unusual” if the realtor sold 7 houses in one month?  Why or why not?

 

 

  1.  (35 points) In a small town in Illinois, there is a 0.80 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected.  Show your work to receive partial credit.

 

22.A.     (10 points) Find the mean and standard deviation in the number of people with brown eyes from the randomly selected group of 13.

 

22.B.     (5 points) Find the probability that all of the selected people have brown eyes.

 

22.C.     (5 points) Find the probability that exactly 12 of the selected people have brown eyes.

 

22.D.     (10 points) Find the probability that the number of selected people that have brown eyes is 11 or more.

 

22.E.      (5 points) Using a critical value of α = 0.05, is 13 an unusually high number for those with brown eyes from a randomly selected group of 13 people?  Why or why not?

 

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