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Sample questions
Chap 1.
1.
The following shows the temperatures (high, low) and weather conditions in a
given Sunday for some selected world cities. For the weather conditions, the
following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly
cloudy.
City
Acapulco
Bangkok
Mexico City
Montreal
Paris
Rome
Toronto
a.
b.
c.
d.
e.
2.
Hi
99
92
77
72
77
88
78
Lo
77
78
57
56
58
68
61
Condition
pc
pc
sh
pc
c
cl
c
How many elements are in this data set?
How many variables are in this data set?
How many observations are in this data set?
Name the variables and indicate whether they are qualitative or quantitative.
For which variables are arithmetic operations appropriate and for which are
they not appropriate?
The following table shows the starting salaries of a sample of recent business
graduates.
Income (In $1,000s)
15 - 19
20 - 24
25 - 29
30 - 34
35 - 39
Number of Graduates
40
60
80
18
2
a. What percentage of graduates in the sample had starting salaries of at least
$30,000?
b. Of the graduates in the sample, what percentage had starting salaries of less
than $25,000?
c. Based on this sample, what percentage of all business graduates do you
estimate to have starting salaries of at least $20,000?
Chap 2.
3.
The frequency distribution below was constructed from data collected from a
group of 25 students.
Height in Inches
58 - 63
64 - 69
70 - 75
76 - 81
82 - 87
88 - 93
94 - 99
Frequency
3
5
2
6
4
3
2
a. Construct a relative frequency distribution.
b. Construct a cumulative frequency distribution.
c. Construct a cumulative relative frequency distribution.
4.
Construct a stem-and-leaf display for the following data.
12
49
5.
52
43
51
45
37
19
47
36
40
32
38
44
26
48
57
22
31
18
For the following observations, indicate what kind of relationship (if any) exist
between x and y.
x
2
6
3
5
4
y
7
19
9
17
11
Chap 3.
6.
The amount of time that a sample of students spends watching television per day
is given below.
Student
1
2
3
4
5
6
7
8
a.
b.
c.
d.
Time
(In Minutes)
40
28
71
48
49
35
40
57
Compute the mean.
Compute the median.
Compute the standard deviation.
Compute the 75th percentile.
7.
In 2002, the average donation to the Community Kitchen was $900 with a
standard deviation of $180. In 2003, the average donation was $1,600 with a
standard deviation of $240. In which year do the donations show a more
dispersed distribution?
8.
The following observations are given for two variables.
y
5
8
18
20
22
30
10
7
a.
b.
c.
d.
x
2
12
3
6
11
19
18
9
Compute and interpret the sample covariance for the above data.
Compute the standard deviation for x.
Compute the standard deviation for y.
Compute and interpret the sample correlation coefficient.
Chap 4.
9.
Assume you have applied for two scholarships, a Merit scholarship (M) and an
Athletic scholarship (A) The probability that you receive an Athletic scholarship is
0.18. The probability of receiving both scholarships is 0.11. The probability of
getting at least one of the scholarships is 0.3.
a. What is the probability that you will receive a Merit scholarship?
b. Are events A and M mutually exclusive? Why or why not? Explain.
c. Are the two events A, and M, independent? Explain, using probabilities.
d. What is the probability of receiving the Athletic scholarship given that you
have been awarded the Merit scholarship?
e. What is the probability of receiving the Merit scholarship given that you
have been awarded the Athletic scholarship?
10.
The probability of an economic decline in the year 2000 is 0.23. There is a
probability of 0.64 that we will elect a republican president in the year 2000. If
we elect a republican president, there is a 0.35 probability of an economic decline.
Let “D” represent the event of an economic decline, and “R” represent the event
of election of a Republican president.
a. Are “R” and “D” independent events?
b. What is the probability of a Republican president and economic decline in the
year 2000?
c. If we experience an economic decline in the year 2000, what is the probability
that there will a Republican president?
d. What is the probability of economic decline or a Republican president in the
year 2000? Hint: You want to find P(D  R).
11.
A bank has the following data on the gender and marital status of 200 customers.
Single
Married
a.
b.
c.
d.
e.
f.
g.
Male
20
100
Female
30
50
What is the probability of finding a single female customer?
What is the probability of finding a married male customer?
If a customer is female, what is the probability that she is single?
What percentage of customers is male?
If a customer is male, what is the probability that he is married?
Are gender and marital status mutually exclusive?
Is marital status independent of gender? Explain using probabilities.
12..
Records of a company show that 20% of the employees have only a high school
diploma; 70% have bachelor degrees; and 10% have graduate degrees. Of those
with only a high school diploma, 10% hold management positions; whereas, of
those having bachelor degrees, 40% hold management positions. Finally, 80% of
the employees who have graduate degrees hold management positions.
a. What percentage of employees holds management positions?
b. Given that a person holds a management position, what is the probability that
she/he has a graduate degree?
#42 (textbook p. 174) – Answer key is in the back of the textbook.
#44 (textbook p. 175) – Answer key is in the back of the textbook.
Chap 5.
13.
For the following probability distribution:
x
0
1
2
3
4
5
6
7
8
9
10
f(x)
0.01
0.02
0.10
0.35
0.20
0.11
0.08
0.05
0.04
0.03
0.01
a. Determine E(x).
b. Determine the variance and the standard deviation.
14.
The records of a department store show that 20% of its customers who make a
purchase return the merchandise in order to exchange it. In the next six purchases,
a. what is the probability that three customers will return the merchandise for
exchange?
b. what is the probability that four customers will return the merchandise for
exchange?
c. what is the probability that none of the customers will return the merchandise
for exchange?
15.
On the average, 6.7 cars arrive at the drive-up window of a bank every hour.
Define the random variable X to be the number of cars arriving in any hour.
a. What is the appropriate probability distribution for X? Explain how X
satisfies the properties of the distribution.
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.
Chap 6.
16.
The time it takes to hand carve a guitar neck is uniformly distributed between 110
and 190 minutes.
a. What is the probability that a guitar neck can be carved between 95 and 165
minutes?
b. What is the probability that the guitar neck can be carved between 120 and
200 minutes?
c. Determine the expected completion time for carving the guitar neck.
d. Compute the standard deviation.
17.
Scores on a recent national statistics exam were normally distributed with a mean
of 80 and a standard deviation of 6.
a. What is the probability that a randomly selected exam will have a score of at
least 71?
b. What percentage of exams will have scores between 89 and 92?
c. If the top 2.5% of test scores receive merit awards, what is the lowest score
eligible for an award?
d. If there were 334 exams with scores of at least 89, how many students took
the exam?
18.
A manufacturing process produces items whose weights are normally distributed.
It is known that 22.57% of all the items produced weigh between 100 grams up to
the mean and 49.18% weigh from the mean up to 190 grams. Determine the
mean and the standard deviation.
19.
The price of a stock is uniformly distributed between $30 and $40.
a.
b.
c.
d.
e.
20.
What is the probability that the stock price will be more than $37?
What is the probability that the stock price will be less than or equal to $32?
What is the probability that the stock price will be between $34 and $38?
Determine the expected price of the stock.
Determine the standard deviation for the stock price.
The records show that 8% of the items produced by a machine do not meet the
specifications. Use the normal approximation to the binomial distribution to
answer the following questions. What is the probability that a sample of 100 units
contains
a. Five or more defective units?
b. Ten or fewer defective units?
c. Eleven or less defective units?
21.
The time it takes a mechanic to change the oil in a car is exponentially distributed
with a mean of 5 minutes.
a. What is the probability density function for the time it takes to change the oil?
b. What is the probability that it will take a mechanic less than 6 minutes to
change the oil?
c. What is the probability that it will take a mechanic between 3 and 5 minutes to
change the oil?
d. What is the variance of the time it takes to change the oil?
Chap 7.
22.
A population of 1,000 students spends an average of $10.50 a day on dinner. The
standard deviation of the expenditure is $3. A simple random sample of 64
students is taken.
a. What are the expected value, standard deviation, and shape of the sampling
distribution of the sample mean?
b. What is the probability that these 64 students will spend a combined total of
more than $715.21?
c. What is the probability that these 64 students will spend a combined total
between $703.59 and $728.45?
23.
A simple random sample of 6 recent graduates revealed the following information
about their weekly incomes.
Graduates
A
B
C
D
E
F
Weekly Income
$250
270
285
240
255
290
a. What is the point estimate of the expected value of the average weekly
income of all the recent graduates?
b. What is the point estimate of the expected value of the standard deviation for
the population?
24.
The SAT scores have an average of 1200 with a standard deviation of 60. A
sample of 36 scores is selected.
a.
b.
c.
d.
e.
25.
Below you are given the values obtained from a random sample of 4 observations
taken from an infinite population.
32
a.
b.
c.
d.
26.
What is the probability that the sample mean will be larger than 1224?
What is the probability that the sample mean will be less than 1230?
What is the probability that the sample mean will be between 1200 and 1214?
What is the probability that the sample mean will be greater than 1200?
What is the probability that the sample mean will be larger than 73.46?
34
35
39
Find a point estimate for .
Find a point estimate for 2.
Find a point estimate for .
What can be said about the sampling distribution of x ? Be sure to discuss the
expected value, the standard deviation, and the shape of the sampling
distribution of x .
Michael is running for president. The proportion of voters who favor Michael is
0.8. A simple random sample of 100 voters is taken.
a. What are the expected value, standard deviation, and shape of the sampling
distribution of p ?
b. What is the probability that the number of voters in the sample who will not
favor Michael will be between 26 and 30?
c. What is the probability that the number of voters in the sample who will not
favor Michael will be more than 16?
27.
A random sample of ten examination papers in a course that was given on a pass
or fail basis showed the following scores.
Paper Number
1
2
3
4
5
6
7
8
9
10
Grade
65
87
92
35
79
100
48
74
79
91
Status
Pass
Pass
Pass
Fail
Pass
Pass
Fail
Pass
Pass
Pass
a. What is the point estimate for the mean of the population?
b. What is the point estimate for the standard deviation of the population?
c. What is the point estimate for the proportion of all students who passed the
course?