Midterm Exam_MATH302
Part 1 of 9 -
Question 1 of 25
The mode is best described as the
A.same as the average
B.middle observation
C.most frequently
occurring value
D.50th percentile
Part 2 of 9 -
Question 2 of 25
A
jar contains four white marbles, five red marbles, and six black marbles. If a
marble is selected at random, find the
probability that it is white or black .
A.2/15
B.2/3
C.1/5
D.2/5
Question 3 of 25
The formal way to revise probabilities based on new information
is to use:
A.common sense
probabilities
B.unilateral
probabilities
C.complementary probabilities
D.conditional probabilities
Part 3 of 9 -
Question 4 of 25
If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5.
What is the expectation of this game?
A.$3.06
B.-$2.78
C.-$3.06
D.$2.78
Question 5 of 25
Suppose that 50 identical batteries are being tested. After 8 hours of
continuous use, assume that a given battery
is still operating with a probability of 0.70 and has failed with a
probability of 0.30.
What is the probability that between 25 and 30 batteries
(inclusive) will last at least 8 hours?
A.0.7792
B.0.1186
C.0.0839
D.0.9169
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Question 6 of 25
A drug is reported to benefit 40% of the patients who take it. If 6
patients take the drug, what is the probability that 4 or more patients will
benefit?
A.0.667
B.0.179
C.0.138
D.0.862
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Part 4 of 9 -
Question 7 of 25
Find the probability, P(Z < 0.17), using the standard
normal distribution.
A..8300
B..4325
C..5675
D..0675
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Question 8 of 25
Given that Z is a standard normal variable, the value z for
which P(Z < z) = 0.2580 is
A.-0.65
B.-0.70
C.0.242
D.0.758
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Question 9 of 25
The average height of flowering cherry trees in a nursery is
11 feet. If the heights are normally distributed with a standard deviation of 1.6, find the probability that a randomly
selected cherry tree in this nursery is
less than 13 feet tall.
A. 0.67
B.0.89
C.0.95
D.0.11
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Question 10 of 25
If Z is a standard normal random variable, the area between
z = 0.0 and z =1.30 is 0.4032, while the area between z =
0.0 and z = 1.50 is 0.4332. What is the area between z =
-1.30 and z = 1.50?
A.0.8364
B.0.0668
C.0.0968
D.0.0300
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Question 11 of 25
Given that the random variable X is normally distributed with a mean of 80
and a standard deviation of 10, P(85
< X <
90) is
A.0.5328
B.0.3413
C.0.1498
D.0.1915
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Question 12 of 25
In a normal distribution,
changing the standard deviation:
A.makes the curve more robust
B.shifts the curve left or right
C.makes the curve more or less spread out
D.splits the distribution to two curves
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Part 5 of 9 -
Question 13 of 25
Accepted characters: numbers,
decimal point markers (period or comma),
sign indicators (-), spaces (e.g., as
thousands separator, 5 000), "E" or "e" (used in scientific
notation). NOTE: For scientific
notation, a period MUST be used as the
decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Suppose that an analysis of a set of test scores reveals that: .
Compute the interquartile range. Place your answer, rounded to 1 decimal
place, in the blank. For example, 32.1
would be a legitimate entry.
Part 6 of 9 -
Question 14 of 25
Accepted
characters: numbers, decimal point
markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
The following data
were obtained from a survey of
college students. The variable X represents the number of non-assigned
books read during the past six months.
x 0 1 2 3 4 5 6
P (X=x) 0.55 0.15 0.10 0.10 0.04 0.03 0.03
What is the standard deviation of X?
Place your answer, rounded to two decimal places in the blank. For example, 4.56
would be a legitimate entry.
Question 15 of 25
Accepted
characters: numbers, decimal point
markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
A DVD rental business determines that customers will rent X
number of DVDs according to the following distribution:
Number of DVDs rented
X 1 2 3 4 5
Probability P(X) 0.15 0.25 0.3 0.25 0.05
What is the mean number of DVDs that customers rent? Round
your answer to one decimal place
as necessary. For example, 4.5 would be a legitimate entry.
Part 7 of 9 -
Question 16 of 25
Accepted characters: numbers, decimal
point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi) where "a" and "b" need to
have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Mothers Against Drunk
Driving (MADD) is a very visible group whose main focus is to educate the
public about the harm caused by drunk drivers. A study was recently done
that emphasized the problem we
all face with drinking and driving. Five hundred accidents that occurred on a
Saturday night were
analyzed. Two items noted
were the number of vehicles involved and whether alcohol played a role
in the accident. The numbers are shown
below:
Number of Vehicles Involved
200
300
Given that alcohol was not involved, what proportion of the accidents involved a single
vehicle? Place your answer, rounded to 2
decimal places, in the blank. For
example, 0.23 is a legitimate
answer.
Question 17 of 25
Accepted characters:
numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g.,
as thousands separator, 5 000), "E" or "e" (used in
scientific notation). NOTE: For
scientific notation, a period MUST be
used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Mothers Against Drunk Driving (MADD) is a very visible
group whose main focus is to educate the public about
the harm caused by drunk drivers.
A study was recently done
that emphasized the problem
we all face with drinking and
driving. Five hundred accidents
that occurred on a
Saturday night were analyzed. Two items noted were
the number of vehicles
involved and whether alcohol played a role in the
accident.
The numbers are shown
below:
Number of Vehicles Involved
200
300
What proportion of
accidents involved alcohol or a single vehicle?
Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a
legitimate entry.
Part 8 of 9 -
Question 18 of 25
Accepted
characters: numbers, decimal point
markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Mrs. Smith's reading
class can read a mean of 175 words per
minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a
special award.
Assuming that the distribution of words read per minute
are normally distributed, what is the minimum number of words per minute
a student would have to read in order to get the award? Place your answer,
rounded to the nearest whole number, in
the
blank. When entering your answer do not
use any labels or
symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry.
Question 19 of 25
Accepted
characters: numbers, decimal point
markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
A popular retail
store knows that the purchase amounts by
its customers is a random variable that
follows a normal distribution with a mean of $30 and a standard deviation of
$9.
What is the probability that a randomly selected customer will spend less than
$15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456
would be a legitimate entry.
Question 20 of 25
Accepted
characters: numbers, decimal point
markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Scores on a mathematics examination appear to follow a
normal distribution with mean of 65 and standard deviation of
15. The instructor
wishes to give a grade of āCā to students scoring between the 60th and 70th percentiles on the
exam.
What score represents the 70th percentile score on the
mathematics exam? Place your answer in the blank, rounded to a whole number.
For example, 62 would be a legitimate entry.
Question 21 of 25
Accepted characters: numbers, decimal
point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b" need
to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
The average hourly wage
of workers at a fast food
restaurant is $6.50/hr with a standard
deviation of $0.45. Assume that the distribution is normally
distributed. If a worker at this fast food restaurant is selected at random,
what is the probability that the worker earns more than $6.75? Place your answer, rounded to 4
decimal places, in the blank. For
example, 0.1776 would be a legitimate entry.
Question 22 of 25
Accepted characters: numbers, decimal
point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
The length of time to complete a door assembly on an
automobile factory assembly line is normally distributed with mean 6.7 minutes and standard
deviation 2.2 minutes. For a
door selected at random, what is the probability the
assembly line time will be between 5 and 10 minutes? Place your answer, rounded
to 4 decimal places, in the blank. For
example, 0.1776 would be a legitimate answer.
Question 23 of 25
Accepted characters: numbers, decimal
point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E"
or "e" (used in scientific notation).
NOTE: For scientific notation, a
period MUST be used as the decimal point marker.
Complex numbers
should be in the form (a + bi)
where "a" and "b"
need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.
Suppose that the average weekly earnings for employees in
general automotive repair shops is $450,
and that the standard deviation
for the weekly earnings for such
employees is $50. A sample of 100 such
employees is selected at random.
Find the probability that the mean of the sample is between
$445 and $455. Place your answer,
rounded to 4 decimal places, in the blank. For example, 0.2345 would be a
legitimate entry.
Part 9 of 9 -
Question 24 of 25
Using the standard normal curve, the Z- score representing the 10th percentile
is 1.28.
True
False
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Question 25 of 25
If Z is a standard normal variable, then P(Z > 1.50) =
0.9332
True
False
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