Note: This is designed to be a sample of the types of questions that could appear.
1.
Students from a statistics class were asked to record their heights in inches. The heights
were recorded as follows:
6
5
52
48
72
63
75
65 61
67 64 74 62
60 69 66
55
67 80
73
74 64 71
50
65a.
Find the mean, median, mode and standard deviation of this data set. Where
rounding is necessary, round to one decimal place.
b.
Interpret the median in a sentence.
c. O
rganize this data into a frequency table using a first lower class limit of 40
and a
class width of 10
.
d. Draw a histogram of the data using the frequency table in part b.
e. B
ased on the histogram, how would you describe the shape of this data set?
f. Find the five number summary of this data set.
g. Interpret the first quartile in a sentence.
h. Use the IQR method to determine if the data set contains any outliers.
i. Draw a boxplot of this data set.
2.
If a data set contains outliers, is the mean or the median the better choice to represent
the center of the data set? Explain your response.3.
Define the terms sample and population and explain the difference between the two.
4.
A
ssume that 15
% of all college students participate in a team sport. In a random sample
of 50 students at a university,
a. What is the probability that exactly 10 participate in a team sport. Round to four
decimal places.b. What is the probability that at least 3 participate in a team sport? Round to four
decimal places.c. What is the expected number that will participate in a team sport in a sample of
50? What is the standard deviation in the number that will participate in a team
sport in a sample of 50?
d. Would it be unusual for 15 of 50 to participate in a team sport? Justify your
response.
5.
The probability distribution given below is for the number of magazine subscriptions for
households in a given city. The random variable X = number of magazine subscriptions.
X 1 2 3 4 5P(X)
0.10
0.15
0.30
0.25
a. Is this a discrete or continuous distribution? Why?
b. Complete the table by finding P(5).
c. Find the expected number of magazine subscriptions.
d. Find the standard deviation in the number of magazine subscriptions.
6.
Consider the following table for blood types.
Blood Group
Males
Females
TotalOAB
AB2017
582018
754035
1510Total 50 50 100
a. What is the probability that a randomly selected person has blood type B?
b. What is the probability that a randomly selected person is female or has
blood type AB?
c. What is the probability that a randomly selected person is male and has
blood type O?
d. Is it unusual for a person to be male and have blood type O? Why or why
not?
7.
The serum cholesterol levels of college students follows a normal distribution with a
mean of 176 mg/dLi and has a standard deviation of 30 mg/dLi.
a. What is the probability that a randomly selected college student has a serum
cholesterol level above 120 mg/dLi? Round to three decimal places.
b. What percentage of college students have a serum cholesterol level between
188 mg/dLi and 240 mg/dLi? Round to three decimal places.
c. 95% of college students have a serum cholesterol level less than what value.
Round to two decimal places.
8.
The time taken to assemble a car in a certain plant is a random variable with a normal
distribution with a mean of 20 hours and a standard deviation of 1.2 hours.
a. What is the probability that a randomly chosen car has an assembly time
between 18.8 hours and 21.4 hours?
b. What is the probability that if a sample of 35 cars is chosen that the mean
assembly time is between 18.8 hours and 21.4 hours?
9.
A calculus class has a mean exam score of 80 with a standard deviation of 15.
Assume
that the exams are normally distributed. If the top 20% of the class will earn an A, what
grade is needed to earn an A?
11.
A meteorologist sampled 13 randomly chosen thunderstorms and found they traveled at
a mean speed of 15 miles per hour with a standard deviation of 1.7 miles per hour. Find
a 99% confidence interval for the mean speed of a thunderstorm. Assume that the
distribution is normal. Be sure to write an appropriate conclusion sentence.
12.
A local school board claims that 85% of its students score above 1200 on the SAT. A rival
school board suspects the actual percentage is lower. Of a random sample of 125
students who took the SAT, 100 of them scored above 1200 on the SAT.a. Verify that the sample meets the criteria necessary to compute a confidence
interval and complete a hypothesis test.b. Find the 95% confidence interval for the proportion of students in the district
who scored above 1200 on the SAT.
c. At the 0.05 level of significance test the claim that less than 85% of the students
scored above 1200 on the SAT.d. Do you believe that the school board was exaggerating when they said 85% score
above 1200? Explain and support your response.
13.
A study is conducted to determine if shoppers spend less when they pay with cash than
when they pay with a credit card. A random sample of 10 shoppers that paid with cash
and 10 shoppers that paid with credit was collected. The data is given below, all values
are in dollars. Assume that the data is normally distributed.
Cash:
10.76
6.26
18.98
11.36
6.78
21.76
8.90
15.64
13.78
9.21
Credit:
16.78
23.89
13.89
15.54
10.36
12.76
18.32
20.67
18.36
19.16
a. Verify that the samples meet the necessary criteria to compute a confidence
interval and complete a hypothesis test.b. Construct the 95% confidence interval for the difference in the mean amount
spent with cash and a credit card. Be sure to give both the sentence and
conclusion.
c. At the 0.05 level of significance, test the claim that customers spend less than
they pay with cash.
14.
Y
ou wish to determine the proportion of Los Angeles County residents who have been
to the Santa Monica Pier in the last year. How many should you survey to be 94%
confident that you find the true proportion to within 3%?
15. The following data represent the number of days absent, x, and the final grade, y, for a
sample of college students in a general education course.
X 0 1 2 3 4 5 6 7 8 9Y 89.2
86.4
83.5
81.1
78.2
73.9
64.3
81.8
65.5
66.2
a. Draw a scatterplot of this data set.
b. Is there a positive, negative or no relationship between number of days absent and
final grade?
c. Does there appear there could be a linear relationship between number of days
absent and final grade?
d. Find the linear correlation coefficient, r. Round to three decimal places.
e. Perform the appropriate hypothesis test to determine whether there is a linear
relationship between number of days absent and final grade. Show all appropriate
parts.
f. Find the least-squares regression line treating the number of absences as the
explanatory variable. Round the slope and y-intercept to three decimal places.
g. Interpret the slope and y-intercept in sentences, if appropriate.
h. Predict the final grade for a student who misses 5 classes and compute the residual.
Did the regression line overestimate or underestimate the final grade?
i. Draw the least-squares regression line on the scatterplot you drew in part a.
j.
Would it be reasonable to use the regression line to estimate the final grade for a
student with 20 absences? Why or why not?
Math 54+54C
Final Practice
Name______________________________
Instructor____________________________
Date________________________________
Math 54 – Practice Final Exam (Written by Professor Hancock)
Note: This is designed to be a sample of the types of questions that could appear on the exam.
Do not expect questions on the actual exam to be identical or just like these questions.
1. Students from a statistics class were asked to record their heights in inches. The heights
were recorded as follows:
65
52
48
72
63
75
65
61
67
64
74
62
60
69
66
55
67
80
73
74
64
71
50
65
a. Find the mean, median, mode and standard deviation of this data set. Where
rounding is necessary, round to one decimal place.
b. Interpret the median in a sentence.
c. Organize this data into a frequency table using a first lower class limit of 40 and a
class width of 10.
d. Draw a histogram of the data using the frequency table in part b.
e. Based on the histogram, how would you describe the shape of this data set?
f. Find the five number summary of this data set.
g. Interpret the first quartile in a sentence.
h. Use the IQR method to determine if the data set contains any outliers.
i. Draw a boxplot of this data set.
2. If a data set contains outliers, is the mean or the median the better choice to represent
the center of the data set? Explain your response.
3. Define the terms sample and population and explain the difference between the two.
4. Assume that 15% of all college students participate in a team sport. In a random sample
of 50 students at a university,
a. What is the probability that exactly 10 participate in a team sport. Round to four
decimal places.
b. What is the probability that at least 3 participate in a team sport? Round to four
decimal places.
c. What is the expected number that will participate in a team sport in a sample of
50? What is the standard deviation in the number that will participate in a team
sport in a sample of 50?
d. Would it be unusual for 15 of 50 to participate in a team sport? Justify your
response.
5. The probability distribution given below is for the number of magazine subscriptions for
households in a given city. The random variable X = number of magazine subscriptions.
X
P(X)
a.
b.
c.
d.
1
0.10
2
0.15
3
0.30
4
0.25
5
Is this a discrete or continuous distribution? Why?
Complete the table by finding P(5).
Find the expected number of magazine subscriptions.
Find the standard deviation in the number of magazine subscriptions.
6. Consider the following table for blood types.
Blood Group
O
Males
20
Females
20
Total
40
A
17
18
35
B
5
7
15
AB
Total
8
50
5
50
10
100
a. What is the probability that a randomly selected person has blood type B?
b. What is the probability that a randomly selected person is female or has
blood type AB?
c. What is the probability that a randomly selected person is male and has
blood type O?
d. Is it unusual for a person to be male and have blood type O? Why or why
not?
7. The serum cholesterol levels of college students follows a normal distribution with a
mean of 176 mg/dLi and has a standard deviation of 30 mg/dLi.
a. What is the probability that a randomly selected college student has a serum
cholesterol level above 120 mg/dLi? Round to three decimal places.
b. What percentage of college students have a serum cholesterol level between
188 mg/dLi and 240 mg/dLi? Round to three decimal places.
c. 95% of college students have a serum cholesterol level less than what value.
Round to two decimal places.
8. The time taken to assemble a car in a certain plant is a random variable with a normal
distribution with a mean of 20 hours and a standard deviation of 1.2 hours.
a. What is the probability that a randomly chosen car has an assembly time
between 18.8 hours and 21.4 hours?
b. What is the probability that if a sample of 35 cars is chosen that the mean
assembly time is between 18.8 hours and 21.4 hours?
9. A calculus class has a mean exam score of 80 with a standard deviation of 15. Assume
that the exams are normally distributed. If the top 20% of the class will earn an A, what
grade is needed to earn an A?
11. A meteorologist sampled 13 randomly chosen thunderstorms and found they traveled at
a mean speed of 15 miles per hour with a standard deviation of 1.7 miles per hour. Find
a 99% confidence interval for the mean speed of a thunderstorm. Assume that the
distribution is normal. Be sure to write an appropriate conclusion sentence.
12. A local school board claims that 85% of its students score above 1200 on the SAT. A rival
school board suspects the actual percentage is lower. Of a random sample of 125
students who took the SAT, 100 of them scored above 1200 on the SAT.
a. Verify that the sample meets the criteria necessary to compute a confidence
interval and complete a hypothesis test.
b. Find the 95% confidence interval for the proportion of students in the district
who scored above 1200 on the SAT.
c. At the 0.05 level of significance test the claim that less than 85% of the students
scored above 1200 on the SAT.
d. Do you believe that the school board was exaggerating when they said 85% score
above 1200? Explain and support your response.
13. A study is conducted to determine if shoppers spend less when they pay with cash than
when they pay with a credit card. A random sample of 10 shoppers that paid with cash
and 10 shoppers that paid with credit was collected. The data is given below, all values
are in dollars. Assume that the data is normally distributed.
Cash:
10.76 6.26
18.98 11.36 6.78
21.76 8.90
15.64 13.78 9.21
Credit:
16.78 23.89 13.89 15.54 10.36 12.76 18.32 20.67 18.36 19.16
a. Verify that the samples meet the necessary criteria to compute a confidence
interval and complete a hypothesis test.
b. Construct the 95% confidence interval for the difference in the mean amount
spent with cash and a credit card. Be sure to give both the sentence and
conclusion.
c. At the 0.05 level of significance, test the claim that customers spend less than
they pay with cash.
14. You wish to determine the proportion of Los Angeles County residents who have been
to the Santa Monica Pier in the last year. How many should you survey to be 94%
confident that you find the true proportion to within 3%?
15. The following data represent the number of days absent, x, and the final grade, y, for a
sample of college students in a general education course.
X
Y
0
89.2
1
86.4
2
83.5
3
81.1
4
78.2
5
73.9
6
64.3
7
81.8
8
65.5
9
66.2
a. Draw a scatterplot of this data set.
b. Is there a positive, negative or no relationship between number of days absent and
final grade?
c. Does there appear there could be a linear relationship between number of days
absent and final grade?
d. Find the linear correlation coefficient, r. Round to three decimal places.
e. Perform the appropriate hypothesis test to determine whether there is a linear
relationship between number of days absent and final grade. Show all appropriate
parts.
f. Find the least-squares regression line treating the number of absences as the
explanatory variable. Round the slope and y-intercept to three decimal places.
g. Interpret the slope and y-intercept in sentences, if appropriate.
h. Predict the final grade for a student who misses 5 classes and compute the residual.
Did the regression line overestimate or underestimate the final grade?
i. Draw the least-squares regression line on the scatterplot you drew in part a.
j. Would it be reasonable to use the regression line to estimate the final grade for a
student with 20 absences? Why or why not?
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