Midterm  Exam_MATH302

 

 

Part 1 of 9 -

 

Question 1 of 25                                                                                                                                                                               1.0 Points
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                                                                                                                                                                               1.0 Points 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                                                                                                                                                                               1.0 Points
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                                                                                                                                                                               1.0 Points
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                                                                                                                                                                               1.0 Points 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                                                                                                                                                                               1.0 Points 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                                                                                                                                                                               1.0 Points
Find the probability, P(Z < 0.17), using the standard normal  distribution.

A..8300

B..4325

C..5675

D..0675

 

Question 8 of 25                                                                                                                                                                               1.0 Points
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                                                                                                                                                                               1.0 Points
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                                                                                                                                                                             1.0 Points
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                                                                                                                                                                             1.0 Points
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                                                                                                                                                                             1.0 Points
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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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.

Answer:

 


Part 7 of 9 -

 

Question 16 of 25                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points 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                                                                                                                                                                             1.0 Points
Using the standard normal curve,  the Z- score representing the 10th percentile is 1.28.

True

False

 


Question 25 of 25                                                                                                                                                                             1.0 Points
If Z is a standard normal variable, then P(Z > 1.50) = 0.9332

True

False

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