Math 302 Midterm Exam | Complete Solution

Question 1 of 25    1.0 Points
An advertisement for a car states that it is 10% more powerful than its competitor. This is an example of

 A.ambiguous averages    
 B.changing the subject

 C.suspect samples

 D.detached statistics

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Part 2 of 9 -

Question 2 of 25    1.0 Points
A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is

 A.5

 B.8

 C.15

 D.30

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Question 3 of 25    1.0 Points
If two events are mutually exclusive, what is the probability that both occur at the same time?

 A.1.00

 B.Cannot be determined from the information given.    
 C.0.00

 D.0.50

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Part 3 of 9 -

Question 4 of 25    1.0 Points
In one town 33% of the households have a vehicle with all-wheel drive. If 4 households are selected at random, what is the probability that all 4 have vehicles with all-wheel drive?

 A.0.4662

 B.0.0825

 C.0.0119

 D.0.33

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Question 5 of 25    1.0 Points
Which term is NOT synonymous with the expected value of a discrete probability distribution?

 A.variance

 B.mean

 C.μ

 D.theoretical average

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Question 6 of 25    1.0 Points
Find the variance of the following probability distribution.
X    P(X)
1    0.30
2    0.15
3    0.05
4    0.25
5    0.25

 A.1.73

 B.1.61

 C.2.60

 D.1.27

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Part 4 of 9 -

Question 7 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.0.0300

 B.0.0968

 C.0.8364

 D.0.0668

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Question 8 of 25    1.0 Points
The standard deviation of a probability distribution must be:

 A.less than the value of the mean

 B.a negative number

 C.a nonnegative number

 D.a number between 0 and 1

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Question 9 of 25    1.0 Points
If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

 A.equal to the mean

 B.one standard deviation higher than the mean

 C.to the left of the mean

 D.to the right of the mean

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Question 10 of 25    1.0 Points
The mean of a probability distribution is a:

 A.measure of skewness of the distribution    
 B.measure of central location

 C.measure of relative likelihood

 D.measure of variability of the distribution    
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Question 11 of 25    1.0 Points
The standard deviation of a probability distribution is a:

 A.measure of central location
    
 B.measure of relative likelihood

 C.measure of variability of the distribution    
 D.measure of skewness of the distribution    
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Question 12 of 25    1.0 Points
The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:

 A.point estimate theorem

 B.central tendency theorem

 C.simple random sample theorem

 D.central limit theorem

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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.

The histogram below represents scores achieved by 250 job applicants on a personality profile.

What percentage of the job applicants scored between 30 and 40?  Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer.
 

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.

In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank  and place the variance in the second blank.  

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.
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

Find P(X > 0). Place your answer, rounded to two decimal places in the blank. For example, 0.56 would be a legitimate entry.  

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.

A restaurant menu has a price-fixed complete dinner that consists of an appetizer, entrée, beverage, and dessert. You have a choice of five appetizers, ten entrees, three beverages, and six desserts. How many possible complete dinners are possible? Place your answer, as a whole number—no decimal places—in the blank. For example 176 would be a legitimate entry  

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.

An urn contains 12 balls identical in every respect except their color. There are 3 red balls, 7 green balls, and 2 blue balls. You draw two balls from the urn, but replace the first ball before drawing the second. Find the probability that the first ball drawn is red and the second ball drawn is green. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.4567 would be 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.

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 probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 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.

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 $20 or more at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 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.

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.  

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.

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

Only 5% of the students taking the test scored higher than what value? Place your answer, rounded to a whole number, in the blank. For example, 78 would be a legitimate entry.  

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.

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 are the two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values? Place your answers in the blanks provided. Do not include a dollar sign. For example, 14.25 would be a legitimate entry.

Lower value  
Upper value  

Part 9 of 9 -

Question 24 of 25    1.0 Points
Using the standard normal curve, the Z- score representing the 5th percentile is 1.645.

 True

 False

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Question 25 of 25    1.0 Points
Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.

 True

 False

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