Statistics exams | Mathematics homework help

Question 1 of 25

1.0 Points

Since the population is always larger than the sample, the population mean:

 

[removed]A.is always larger than or equal to the sample mean

 

[removed]B.can be smaller than, or larger than, or equal to the sample mean

 

[removed]C.is always smaller than or equal to the sample mean

 

[removed]D.is always strictly less than the sample mean

 

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Question 2 of 25

1.0 Points

If two events are mutually exclusive, what is the probability that both occur at the same time?

 

[removed]A.0.00

 

[removed]B.Cannot be determined from the information given.

 

[removed]C.0.50

 

[removed]D.1.00

 

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Question 3 of 25

1.0 Points

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

 

[removed]A.2/5

 

[removed]B.5/8

 

[removed]C.1/4

 

[removed]D.1/8

 

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Question 4 of 25

1.0 Points

The binomial probability distribution is used with

 

[removed]A.a continuous random variable

 

[removed]B.a discrete random variable

 

[removed]C.either a discrete or a continuous random variable, depending on the sample size

 

[removed]D.either a discrete or a continuous random variable, depending on the variance

 

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Question 5 of 25

1.0 Points

We assume that the outcomes of successive trials in a binomial experiment are:

 

[removed]A.identical from trial to trial

 

[removed]B.probabilistically dependent

 

[removed]C.random numbers between 0 and 1

 

[removed]D.probabilistically independent

 

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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 25 batteries will last at least 8 hours?

 

[removed]A.0.0024

 

[removed]B.0.0009

 

[removed]C.0.9991

 

[removed]D.0.8967

 

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Question 7 of 25

1.0 Points

Find the probability, P(Z < 0.17), using the standard normal distribution.

 

[removed]A..8300

 

[removed]B..4325

 

[removed]C..5675

 

[removed]D..0675

 

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Question 8 of 25

1.0 Points

The normal distribution is:

 

[removed]A.the single most important distribution in statistics

 

[removed]B.a density function of a discrete random variable

 

[removed]C.a binomial distribution with only one parameter

 

[removed]D.a discrete distribution

 

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Question 9 of 25

1.0 Points

The standard deviation of a probability distribution is a:

 

[removed]A.measure of variability of the distribution

 

[removed]B.measure of relative likelihood

 

[removed]C.measure of skewness of the distribution

 

[removed]D.measure of central location 

 

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Question 10 of 25

1.0 Points

Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is

 

[removed]A.0.8413

 

[removed]B.0.0919

 

[removed]C.0.9332

 

[removed]D.0.7745

 

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Question 11 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?

 

[removed]A.one standard deviation higher than the mean

 

[removed]B.to the left of the mean

 

[removed]C.equal to the mean

 

[removed]D.to the right of the mean

 

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Question 12 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

 

[removed]A.0.5328

 

[removed]B.0.1915

 

[removed]C.0.1498

 

[removed]D.0.3413

 

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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 below 60?  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.

[removed]

 

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 annual returns, in percentages, on stocks A and B for three possible states of the economy are given in the table below.

 

Economy State

Probability

StockA

StockB

Good

0.5

40

20

Average

0.3

20

40

Bad

0.2

10

8

If one invested in StockA, what would be the expected annual percentage return? Place your answer, in percent, in the blank. For example, an expected 10 percent return would be recorded as 10. Do not use a percent sign.  [removed]

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

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. [removed]

 

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. 

Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that neither of the questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. [removed]

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

Did alcohol play a role?

1

2

3

 

Yes

60

110

30

200

No

40

215

45

300

 

100

325

75

 

What proportion of accidents involved more than one vehicle?  Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.  [removed]

 

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.

In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

 

Place your answer, rounded to four decimal places, in the blank.  [removed]  When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 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. 

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank. [removed]

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 $30 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. [removed]

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 greater than $460. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate answer.[removed]

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.  [removed]

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. [removed]

 

Question 24 of 25

1.0 Points

Using the standard normal curve, the Z- score representing the 85th percentile is 0.67

 

[removed]True

[removed]False

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Question 25 of 25

1.0 Points

The left half under the normal curve is slightly smaller than the right half.

 

[removed]True

[removed]False

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