MATH302 -Midterm Exam

Category: Mathematics

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

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

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

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

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

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

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

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

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
P (X=x)

0
0.55

1
0.15

2
0.10

3
0.10

4
0.04

5
0.03

6
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
Probability P(X)

1

2

3

4

5

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
Did alcohol play a role?
Yes
No

1
60
40
100

2
110
215
325

3
30
45
75

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

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
Did alcohol play a role?
1
2
3
200
Yes
60
110
30
300
No
40
215
45
100
325
75
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 When entering your answer do not use any labels or blank.
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 “C” 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

Question 25 of 25
If Z is a standard normal variable, then P(Z > 1.50) = 0.9332
True
False

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