MGMT2262 Midterm practice questions
Word to the wise: Be sure you can solve the midterm questions that are posted on mathwizz.com.
Question 1
Given this set of data:
|
20 |
25 |
25 |
32 |
38 |
47 |
49 |
101 |
|
109 |
120 |
125 |
127 |
133 |
133 |
144 |
162 |
a) Create a stem and leaf plot using a leaf unit of 1.
b) What is the mode?
c) What is the range?
d) Compute the coefficient of skewness. Interpret it.
e) Compute the coefficient of variation. If another data set has a coefficient of variation of 29.23%, which data set is more consistent?
f) Does the data contain any outliers?
Question 2
In a survey, 48% of TV viewers are under the age of 30. Of those under the age of 30, 25% watch CSI. Of those aged 30 or over, 75% watch CSI.
a) What is the probability a TV viewer is aged 30 or over or does not watch CSI?
b) What is the probability a TV viewer is under the age of 30 and does not watch CSI?
c) What is the probability a person is either under the age of 30 or a viewer of CSI but not both?
d) Does watching CSI depend on the viewer’s age?
Question 3
A survey of 500 people in Calgary, Edmonton and Red Deer split them into low, medium or high income categories. These are the results:
|
|
Low |
Medium |
High |
Total |
|
Calgary |
55 |
78 |
92 |
225 |
|
Red Deer |
19 |
46 |
10 |
75 |
|
Edmonton |
44 |
82 |
74 |
200 |
|
Total |
118 |
206 |
176 |
500 |
a) What is the probability a person is in the medium income group and does not live in Calgary?
b) What is the probability a person is either in the low or high income group or does not live in Red Deer?
c) Of those who are in either the medium or high income category, what percentage do not live in Red Deer?
d) Does being low income depend on living in Red Deer?
Question 4
a) A (very small) video store has 10 action movies, 5 romantic movies, 4 comedies and 8 dramas. If you choose 3 of each type, how many combinations could you have?
b) A church has 30 members. It needs 5 people for committee A, 8 people for committee B and 12 people for committee C. If no member of the church can serve on more than one committee, how many possible combinations are there?
c) A password of 8 characters must have a letter in the odd positions (1, 3, 5, 7) and a number in the even positions. If no character can repeat and the letter are not case-sensitive, how many possible passwords can be created?
Question 5
In a town, 40% of people watch hockey on TV on average.
a) If 12 people are randomly selected, what is the probability that fewer than 7 of them watch hockey?
b) If 17 people are randomly selected, what is the probability that more than 8 of them watch hockey?
c) If 9 people are selected, what is the probability that exactly 4 of them watch hockey?
d) Suppose the town has 1200 people. If the coefficient of variation for another town is 17.2%, which town has the lower coefficient of variation?
e) For this town of 1200, what is the fewest and most number of people who watch hockey 99.7% of the time? Round to the nearest whole number.
Question 6
The annual percentage rate (APR) of credit cards follows a Beta distribution with a mean of 16.7% and standard deviation of 3.9%.
a) If a sample of 40 credit cards is taken, what is the probability the average rate of these cards is more than 15%?
b) Suppose the standard deviation has changed over time, but the mean remains the same at 16.7%. If a sample of 40 cards is taken, what would the standard deviation need to be if the probability that the average of these 40 cards exceeds 18% is 6.06%?
c) Based on Chebyshev’s Theorem, at least what percentage of the distribution of the credit card rates lies between 11.24% and 22.16%?
Question 7
The accident rate in a certain industry is 1 accident per 10,000 work hours on average.
a) For 50,000 work hours, what is the probability of more than 1 accident?
b) For 75,000 work hours, what is the probability of no more than 4 accidents?
c) Based on Chebyshev’s Theorem, at least 88.89% of the distribution lies between which 2 values based on 75,000 work hours?
Question 8
The annual amount that people give to charity follows a normal distribution with a mean of $532 and standard deviation of $89.
a) What is the probability a person donates more than $550 per year to charity?
b) What is the probability a person donates less than $700 per year to charity?
c) What is the probability a person donates between $600 and $650 per year to charity?
d) What is the cutoff of the top 7.08% given to charity?
e) Between which 2 values would 47.78% of the distribution lie?