Suppose that a histogram of a data set is approximately symmetric | Solution

Part 1 of 9 -

Question 1 of 25    1.0 Points
Suppose that a histogram of a data set is approximately symmetric and "bell shaped". Approximately what percent of the observations are within two standard deviations of the mean?

  A.68%

  B.50%

  C.95%

  D.99.7%

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Part 2 of 9 -

Question 2 of 25    1.0 Points
If A and B are any two events with P(A) = .8 and  then  is:

  A.0.56

  B..24

  C.0.875

  D.0.14

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Question 3 of 25    1.0 Points
Three cards are drawn from a deck without replacement. What is the probability that all three cards are clubs?

  A.0.0129

  B.0.012

  C.0.25

  D.0.0156

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Part 3 of 9 -

Question 4 of 25    1.0 Points
According to an Internet posting, 80% of adults enjoy drinking beer. A group of 7 adults is chosen randomly. The probability that no more than 3 of them enjoy drinking beer is:

  A.0.429

  B.0.033

  C.0.029

  D.0.267

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Question 5 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.0.862

  B.0.138

  C.0.667

  D.0.179

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Question 6 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 fewer than 40 batteries will last at least 8 hours?

  A.0.7986

  B.0.9598

  C.0.9211

  D.0.0789

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Part 4 of 9 -

Question 7 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.simple random sample theorem

  C.central tendency theorem

  D.central limit theorem

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Question 8 of 25    1.0 Points
Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is

  A.0.7745

  B.0.9332

  C.0.0919

  D.0.8413

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Question 9 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

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Question 10 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.splits the distribution to two curves

  D.makes the curve more or less spread out

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Question 11 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.0.758

  B.-0.65

  C.0.242

  D.-0.70

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Question 12 of 25    1.0 Points
The standard deviation of a probability distribution is a:

  A.measure of skewness of the distribution

  B.measure of variability of the distribution

  C.measure of relative likelihood

  D.measure of central location
    
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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.
A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.
 
     Did Well in Exam    Did Poorly in Exam
Studying for Exam    60    15
Went Partying    22    53

Of those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam?  Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitmate 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.

A school determines that the number of children X in the families who attend the school follows the distribution below:
 Number of children X     1    2     3     4     5
 Probability P(X)     0.20     0.35     0.25     0.15     0.05

What is the mean number of children per family?  Round your answer to one decimal place as necessary. For example, 4.5 would be a legitimate entry.

Answer:        

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.

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.   

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
Did alcohol play a role?    1    2    3    
Yes    60    110    30    200
No    40    215    45    300
     100    325    75    

Given that alcohol was not involved, what proportion of the accidents were multiple vehicle?  Place your answer, rounded to 2 decimal places, in the blank.  For example, 0.23 is 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 ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
 
  = chocolate chosen
  = strawberry chosen
  = vanilla chosen
   = ice cream on a cone
 ice cream in a cup

Find the probability that the ice cream was sold on a cone and was chocolate flavor.  Place your answer, rounded to 4 decimal places, in the blank.  For exampe, 0.3456 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.

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 98% 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   

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 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 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.

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 mean of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 123 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.

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 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.

What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 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.

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.   

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

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Question 25 of 25    1.0 Points
A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

  True

  False

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