- points) Which of the four levels of measurement? (nominal, ordinal,? interval, ratio) is most appropriate for salaries of college professors. (Circle one)
- Ordinal
- Nominal
- Interval
- (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)
- Convenience
- Stratified
- Random
- Systematic
- Cluster
- (3 points) ___________________ are sample values that lie very far away from the vast majority of other sample values.
- (3 points) TRUE / FALSE : The mathematical formula for finding is . (Circle one)
- (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)
- Histogram
- Scatter Plot
- Dotplot
- Pie Chart
- (3 points) The ___________________ of a data set is a measure of center indicating the value that occurs with the greatest frequency.
- (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)
- (3 points) TRUE / FALSE : For any event A, the probability of A is between -1 and 1 inclusive. That is, .
- (3 points) For any event , it’s ___________________, denoted by , consists of all outcomes in which event does not occur.
- (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)
- Disjoint
- Mutually Exclusive
- Compound
- All of the Above
- A & B Only
- (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.
- (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)
- Probability Distribution
- Random Variable
- Probability Histogram
- Expected Value
- (3 points) Which of the following is not a requirement of a binomial probability distribution? (Circle one)
- The procedure has a random number of trials.
- The trials must be independent.
- Each trial must have all outcomes classified into two categories (e.g. success and failure).
- The probability of a success remains constant in all trials.
- All of the above are requirements of the binomial probability distribution.
- (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.
- (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)
- P(A and B)
- P(A ?B)
- P(A) * P(B | A)
- All of the above
- A & B only
NOTE: For the following questions, you can use Excel (the data files are available on LEO).
- (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 |
- (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 |
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Class Width =
- (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).
- (4 points) What is the arithmetic mean of the data set?
- (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).
- (3 points) What is the median of the data set?
- (3 points) What is the mode of the data set? Note, if there is more than one mode, list all of them.
- (6 points) What is the standard deviation of the data set?
- (3 points) What is the variance of the data set?
- (5 points) Draw a box-plot graph of the data set. Label each part of the graph.
- (6 points) Draw a Stem Plot (or Stem-and-Leaf Plot) of the data set.
- (5 points) Is a woman who is 72 inches tall considered “unusual”? Why or why not?
- (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.
- (5 points) Using the empirical rule, what temperature range accounts for 68% of healthy adults?
- (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?
- (5 points) Using Chebyshev’s theorem, what temperature range accounts for 75% of healthy adults?
- (5 points) Using Chebyshev’s theorem, what percentage of healthy adults fall within 96.34?F and 100.06?F?
- (5 points) When would we use Chebyshev’s theorem instead of the empirical rule?
- (20 points) Consider the following scenario. A bag contains 4 Red? marbles, 3 Blue? marbles, and 7 Green marbles.
- (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?
- (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?
- (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.
- (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?
- (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 |
- (5 points) Given that an asthma sufferer is an occasional smoker, what is the probability that the person is a woman?
- (5 points) Given that an asthma sufferer is a man, what is the probability that the person is a regular smoker?
- (5 points) Given that an asthma sufferer is a regular smoker, what is the probability that the person is a nonsmoker?
- (10 points) Counting Problems
- (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?
- (5 points) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose? from?
- (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 |
- (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.
- (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.”
- (5 points) What is the probability that the realtor will sell 5 or more houses in one month.
- (5 points) Would it be considered “unusual” if the realtor sold 7 houses in one month? Why or why not?
- (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.
- (10 points) Find the mean and standard deviation in the number of people with brown eyes from the randomly selected group of 13.
- (5 points) Find the probability that all of the selected people have brown eyes.
- (5 points) Find the probability that exactly 12 of the selected people have brown eyes.
- (10 points) Find the probability that the number of selected people that have brown eyes is 11 or more.
- (5 points) Using a critical value of ? = 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?