Download Solve the problem. Round results to the nearest hundredth. 1) The

Redwood High School. Department of Mathematics
2015-2016 Advanced Algebra Stats wkst #3 .
Hard Worker's name:___________________________________
7) A tax auditor selects
every 1000th income tax
return that is received.
Solve the problem. Round results to the nearest
hundredth.
1) The mean of a set of data
1)
is 4.95 and its standard
deviation is 4.01. Find the
z score for a value of 7.56.
2) A department store, on
average, has daily sales of
$28,284.82. The standard
deviation of sales is $1000.
On Tuesday, the store
sold $36,405.18 worth of
goods. Find Tuesday's z
score. Was Tuesday an
unusually good day?
Solve the problem. Round results to the nearest
hundredth.
8) The mean of a set of data
8)
is 1.07 and its standard
deviation is 2.77. Find the
z score for a value of 0.42.
2)
Find the number of standard deviations from the mean.
Round your answer to two decimal places.
9) The annual snowfall in a
9)
town has a mean of 39
inches and a standard
deviation of 12 inches.
Last year there were 61
inches of snow. How
many standard deviations
from the mean is that?
Find the number of standard deviations from the mean.
Round your answer to two decimal places.
3) The annual snowfall in a
3)
town has a mean of 30
inches and a standard
deviation of 10 inches.
Last year there were 67
inches of snow. How
many standard deviations
from the mean is that?
Identify which of these types of sampling is used: random,
stratified, systematic, cluster, convenience.
4) 49, 34, and 48 students are 4)
selected from the
Sophomore, Junior, and
Senior classes with 496,
348, and 481 students
respectively.
5) A sample consists of
every 49th student from a
group of 496 students.
5)
6) A market researcher
selects 500 drivers under
30 years of age and 500
drivers over 30 years of
age.
6)
7)
1
10) In one town, the number
of pounds of sugar
consumed per person per
year has a mean of 5
pounds and a standard
deviation of 1.6 pounds.
Tyler consumed 11
pounds of sugar last year.
How many standard
deviations from the mean
is that?
10)
11) Mario's weekly poker
winnings have a mean of
$328 and a standard
deviation of $52. Last
week he won $194. How
many standard deviations
from the mean is that?
11)
12) The number of hours per
day a college student
spends on homework has
a mean of 6 hours and a
standard deviation of 0.5
hours. Yesterday she
spent 2 hours on
homework. How many
standard deviations from
the mean is that?
12)
Solve the problem.
16) In a survey of 1000
Americans, 850 said that
they own a cell phone.
Assume that the survey
was properly conducted
and that the 1000 people
surveyed represent an
unbiased sample of the
entire population.
Compute a 95%
confidence interval
(expressed using
percents) for this survey.
Find the z-score corresponding to the given value and use
the z-score to determine whether the value is unusual.
Consider a score to be unusual if its z-score is less than
-2.00 or greater than 2.00. Round the z-score to the nearest
tenth if necessary.
13) A test score of 84.6 on a
13)
test having a mean of 71
and a standard deviation
of 8.
14) A body temperature of
96.5° F given that human
body temperatures have a
mean of 98.20° F and a
standard deviation of
0.62°.
Provide an appropriate response.
15) The SAT is an exam used
by colleges and
universities to evaluate
undergraduate
applicants. The test scores
are normally distributed.
In a recent year, the mean
test score was 1480 and
the standard deviation
was 304. The test scores of
four students selected at
random are 1930, 1340,
2150, and 1450.
a) Find the z-scores
that correspond to each
value
b) Determine whether
any of the values are
unusual.
17) In a survey of 1000
Americans, 850 said that
they own a cell phone.
Assume that the survey
was properly conducted
and that the 1000 people
surveyed represent an
unbiased sample of the
entire population.
Compute a 99.7%
confidence interval
(expressed using
percents) for this survey.
14)
16)
17)
As part of a statistics project, a 6th grade teacher brings to
class a container with 300 red marbles and 500 white
marbles which are thoroughly mixed. To figure out how
many marbles in the container are red without actually
counting them all, a student randomly draws 40 marbles
from the container. Of the 40 marbles drawn, 16 are red.
18) The target population consists of
18)
A) the 16 marbles drawn by the
student.
B) the 800 marbles in the
container.
C) the 300 red marbles in the
container.
D) the 40 marbles drawn by the
student.
E) none of these
15)
19) The N-value for this population is
A) 300.
B) 40.
C) 16.
D) 800.
E) none of these
2
19)
20) The sample consists of
A) the 40 marbles drawn by the
student.
B) the 300 red marbles in the
container.
C) the 16 red marbles drawn by
the student.
D) the 800 marbles in the
container.
E) none of these
20)
21) The sampling proportion is
1
A) 37 %.
2
21)
25) The sampling method used in this
example is called
A) stratified sampling.
B) random sampling, but not
simple random sampling.
C) quota sampling.
D) simple random sampling.
E) none of these
As part of a statistics project, a 6th grade teacher brings to
class a container with 200 red marbles and 800 white
marbles which are thoroughly mixed. To figure out how
many marbles in the container are red without actually
counting them all, a student randomly draws 150 marbles
from the container. Of the 150 marbles drawn, 33 are red.
26) The target population consists of
26)
A) the 33 marbles drawn by the
student.
B) the 200 red marbles in the
container.
C) the 150 marbles drawn by
the student.
D) the 1000 marbles in the
container.
E) none of these
1
B) 5 %.
3
1
C) 13 %
3
D) 5%.
E) none of these
22) Suppose that the student is given
the N-value. What is a reasonable
estimate for the number of red
marbles in the container?
A) 480
B) 320
C) 107
D) 300
E) none of these
22)
23) Suppose that the student is given
the N-value. What is a reasonable
estimate for the number of white
marbles in the container?
A) 300
B) 320
C) 107
D) 480
E) none of these
23)
24) The sampling error is most likely
a result of
A) nonresponse bias.
B) a confounding variable.
C) sampling variability.
D) sampling bias.
E) none of these
24)
25)
3
27) The N-value for this population is
A) 150.
B) 1000.
C) 33.
D) 200.
E) none of these
27)
28) The sample consists of
A) the 1000 marbles in the
container.
B) the 200 red marbles in the
container.
C) the 33 red marbles drawn by
the student.
D) the 150 marbles drawn by
the student.
E) none of these
28)
29) The sampling proportion is
A) 75%.
B) 22%.
C) 25%.
D) 15%.
E) none of these
29)
30) Suppose that the student is given
the N-value. What is a reasonable
estimate for the number of red
marbles in the container?
A) 220
B) 33
C) 150
D) 183
E) none of these
30)
31) The sampling method used in this
example is called
A) stratified sampling.
B) random sampling, but not
simple random sampling.
C) simple random sampling.
D) quota sampling.
E) none of these
31)
Use the confidence level and sample data to find a
confidence interval for estimating the population µ.
Round your answer to the same number of decimal places
as the sample mean.
32) Test scores: n = 95, x =
96.0, = 7.2; 99%
confidence
32)
33) Test scores: n = 82, x =
58.4, = 7.5; 98%
confidence
33)
34) A random sample of 78
light bulbs had a mean
34)
life of x = 494 hours with
a standard deviation of
= 37 hours. Construct a
90% confidence interval
for the mean life, µ, of all
light bulbs of this type.
35) A random sample of 112
full-grown lobsters had a
mean weight of 23 ounces
and a standard deviation
of 2.8 ounces. Construct a
98% confidence interval
for the population mean
µ.
35)
4
36) A laboratory tested 90
chicken eggs and found
that the mean amount of
cholesterol was 247
milligrams with = 15.3
milligrams. Construct a
95% confidence interval
for the true mean
cholesterol content, µ, of
all such eggs.
36)
37) 40 packages are randomly
selected from packages
received by a parcel
service. The sample has a
mean weight of 22.2
pounds and a standard
deviation of 2.3 pounds.
What is the 95%
confidence interval for the
true mean weight, µ, of all
packages received by the
parcel service?
37)
38) A group of 69 randomly
selected students have a
mean score of 23.3 with a
standard deviation of 4.5
on a placement test. What
is the 90% confidence
interval for the mean
score, µ, of all students
taking the test?
38)
In order to determine how American undergraduate
college students feel about eliminating spring break in
order to finish spring term a week early, a survey was
conducted. Two hundred undergraduate students from the
University of Miami (FL) were interviewed. Both of the
interviewers hired to conduct the survey were told to
interview 25 freshmen, 25 sophomores, 25 juniors, and 25
seniors. Of the 200 students interviewed, 20% were in
favor of the elimination of spring break, 70% were
opposed, and 10% had no opinion.
39) The target population for this
39)
survey is
A) the 180 students that had an
opinion.
B) the 200 students that were
interviewed.
C) all American undergraduate
college students.
D) all undergraduates at the
University of Miami.
E) none of these
40) The sample for this survey is
A) the 200 students that were
interviewed.
B) all undergraduates at the
University of Miami.
C) the 180 students that had an
opinion.
D) all American undergraduate
college students.
E) none of these
40)
41) Based on the fact that 20% of the
students interviewed were in
favor of the elimination of spring
break, the value 20% is
A) a population.
B) a statistic.
C) a sample.
D) a parameter.
E) none of these
41)
5
42) Which of the following best
describes the parameter in this
situation?
A) The percentage of American
college students that
undergraduates at the
Univeristy of Miami (FL)
represent.
B) The actual percentage of
American college students
that favor the elimination of
spring break.
C) The 20% of students
interviewed that favored the
elimination of spring break.
D) The actual percentage of
students at the University of
Miami (FL) that favor the
elimination of spring break.
E) none of these
42)
43) The results of this survey are
unreliable primarily because of
A) both selection bias and
non-response bias.
B) selection bias only.
C) the absence of a control
group.
D) nonresponse bias only.
E) none of these
43)
44) The sampling proportion in this
survey is
A) 20%.
B) 200/(the number of
American college students).
C) 100%.
D) 200/(the number of
University of Miami, FL
undergraduates).
E) none of these
44)
45) The sampling method used for the
survey is called
A) random sampling.
B) simple random sampling.
C) quota sampling.
D) stratified sampling.
E) none of these
45)
Use a z-Table to determine the percent of data specified.
46) Between z = 1.41 and z =
46)
2.83.
47) Between z = 0.54 and z =
1.91.
47)
48) Between z = -1.68 and z =
1.68.
48)
49) Greater than z = -1.82
49)
50) Less than z = 0.97
50)
56) Less than 690 hours
Solve the problem.
57) Assume that the weights
of quarters are normally
distributed with a mean
of 5.67 g and a standard
deviation 0.070 g. A
vending machine will
only accept coins
weighing between 5.48 g
and 5.82 g. What
percentage of legal
quarters will be rejected?
A child has an enormous jar in which she has been saving
all of her spare change. In order to determine exactly how
much money she has in the jar, she dumps all of the coins
on the floor and counts them. Under the watchful eye of
her mother, she counts 180 pennies, 120 nickels, 100 dimes,
and 80 quarters.
51) If the child were to grab a handful
51)
of 48 coins at random from the jar,
how much money should she
expect it to be worth?
A) $3.78
B) $39.60
C) $4.92
D) $4.80
E) none of these
52) The data collection method used
in this example is called
A) a survey.
B) random sampling.
C) a controlled study.
D) a census.
E) none of these
52)
A company installs 5000 light bulbs, each with an average
life of 500 hours, standard deviation of 100 hours, and
distribution approximated by a normal curve. Find the
percentage of bulbs that can be expected to last the period
of time.
53) At least 500 hours
53)
54) Between 500 hours and
675 hours
54)
55) Between 290 hours and
540 hours
55)
6
56)
57)
58) The average size of the
fish in a lake is 11.4
inches, with a standard
deviation of 3.2 inches.
Find the percentage of
fish longer than 17 inches.
58)
59) A bank's loan officer rates
applicants for credit. The
ratings are normally
distributed with a mean
of 200 and a standard
deviation of 50. If an
applicant is randomly
selected, find the
percentage of applicants
with a rating that is
between 170 and 220.
59)
60) A bank's loan officer rates
applicants for credit. The
ratings are normally
distributed with a mean
of 200 and a standard
deviation of 50. If an
applicant is randomly
selected, find the
percentage of applicants
with a rating that is
between 200 and 275.
60)
61) A study of the amount of
time it takes a mechanic
to rebuild the
transmission for a 2005
Chevrolet Cavalier shows
that the mean is 8.4 hours
and the standard
deviation is 1.8 hours. If
40 mechanics are
randomly selected, find
the probability that their
mean rebuild time
exceeds 7.7 hours.
61)
62) A study of the amount of
time it takes a mechanic
to rebuild the
transmission for a 2005
Chevrolet Cavalier shows
that the mean is 8.4 hours
and the standard
deviation is 1.8 hours. If
40 mechanics are
randomly selected, find
the probability that their
mean rebuild time is less
than 7.6 hours.
62)
63) A final exam in Math 160
has a mean of 73 with
standard deviation 7.8. If
24 students are randomly
selected, find the
probability that the mean
of their test scores is
greater than 78.
63)
64) A final exam in Math 160
has a mean of 73 with
standard deviation 7.8. If
24 students are randomly
selected, find the
probability that the mean
of their test scores is less
than 70.
64)
7
Answer Key
Testname: H ADVALG S2 TEST 8 STATS WKSV 3
1) 0.65
2) 8.12, yes
3) 3.70 standard deviations above the mean
4) Stratified
5) Systematic
6) Stratified
7) Systematic
8) -0.23
9) 1.83 standard deviations above the mean
10) 3.75 standard deviations above the mean
11) 2.58 standard deviations below the mean
12) 8.00 standard deviations below the mean
13) 1.7; not unusual
14) -2.7; unusual
15) a) x = 1930 z 1.48
x = 1340
z -0.46
x = 2150
z 2.20
x = 1450
z -0.10
b) x = 2150 is unusual because its corresponding z-score (2.20) lies more than 2 standard deviations from the mean.
16) 82.8% to 87.2%
17) 81.7% to 88.3%
18) B
19) D
20) A
21) D
22) B
23) D
24) C
25) D
26) D
27) B
28) D
29) D
30) A
31) C
32) 94.1 < µ < 97.9
33) 56.5 < µ < 60.3
34) 487 hr < µ < 501 hr
35) 22 oz < µ < 24 oz
36) 244 mg < µ < 250 mg
37) 21.5 lb < µ < 22.9 lb
38) 22.4 < µ < 24.2
39) C
40) A
41) B
42) B
43) B
44) B
45) C
46) 7.70%
8
Answer Key
Testname: H ADVALG S2 TEST 8 STATS WKSV 3
47) 26.65%
48) 90.70%
49) 96.56%
50) 83.40%
51) A
52) D
53) 50%
54) 46%
55) 63.8%
56) 97.1%
57) 1.96%
58) 4.01%
59) 38.11%
60) 43.32%
61) 0.9931
62) 0.0025
63) 0.0008
64) 0.0301
9