Question 1

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability that a sample mean would exceed 20 hours per week?
A)1.0
B)0.5
C)1.96
D)Cannot be calculated based on the given information.

Accepted Answer

Since the sample mean is already 20, the probability of it exceeding 20 is 0.5 or 50%.

Question 2

Sometimes,sampling from a population may be preferred because collecting statistics may require that products be ___________.

Accepted Answer

The answer of Sometimes,sampling from a population may be preferred...

Question 3

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the standard error of the mean?
A)0.83
B)10
C)0.5
D)2

Accepted Answer

The answer of A group of statistics students decided to...

Question 4

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score between 85 and 115?
A)0.3413
B)0.6826
C)1.00
D)Very likely

Accepted Answer

To find the probability of scoring between 85 and 115, we need to find the area under the normal curve between the z-scores for these two values.

The z-score for 85 is: 
z = (85 - 100) / 15 
z = -1

The z-score for 115 is: 
z = (115 - 100) / 15 
z = 1

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores: 
P(-1 < z < 1) = 0.6826

Therefore, the probability of scoring between 85 and 115 on an IQ test is 0.6826 or 68.26%.

Question 5

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the probability that the mean completion time is between 1 and 2 hours,i.e. ,60 and 120 minutes?
A)Approximately 1
B)0.1664
C)0.8336
D)0.9676

Accepted Answer

The answer of An accounting firm is planning for the...

Question 6

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.You bought four tires.What is the probability that the average mileage of the four tires exceeds 66,000 miles?
A)0.0013
B)0.9987
C)0.4987
D)0.9544

Accepted Answer

The sample mean for four tires will follow a normal distribution with mean (mu) = 60,000 and standard deviation (sigma) = 4,000 / sqrt(4) = 2,000. To find the probability that the average mileage of the four tires exceeds 66,000 miles:

z = (66,000 - 60,000) / 2,000 = 3

Using a standard normal distribution table or calculator, we find that the probability of z being greater than 3 is approximately 0.0013. Therefore, the probability that the average mileage of the four tires exceeds 66,000 miles is 0.0013 or 0.13%.

Question 7

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.Given a class with 25 students,what is the probability that the class' average IQ score is between 85 and 115?
A)0.4987
B)3.00
C)0.0026
D)0.9974

Accepted Answer

The sampling distribution of the sample mean for 25 students will have the same mean (100) but a smaller standard deviation (15/√25 = 3). Using the standard normal distribution, the probability that the sample mean is between 85 and 115 is approximately 0.9974.

Question 8

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire lasts between 54,000 and 66,000 miles?
A)0.4332
B)0.8664
C)1.00
D)Very likely

Accepted Answer

To solve this problem, we need to standardize the values using the formula z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. In this case:

z1 = (54,000 - 60,000) / 4,000 = -1.5
z2 = (66,000 - 60,000) / 4,000 = 1.5

Using a standard normal distribution table, we can find the probability of a value being between -1.5 and 1.5 standard deviations from the mean. The table gives us a probability of 0.8664, which means that there is an 86.64% chance that a truck tire will last between 54,000 and 66,000 miles.

Question 9

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability of finding a sample mean less than 18 hours?
A)0.4820
B)0.4920
C)0.0080
D)0.0180

Accepted Answer

We need to find the z-score first:
z = (x̄ - μ) / (σ / sqrt(n))
z = (18 - 20) / (10 / sqrt(144))
z = -2 / 0.833 = -2.4
Using a standard normal distribution table or calculator, we can find the probability of z-score being less than -2.4 is 0.008. Therefore, the probability of finding a sample mean less than 18 hours is 0.008.

Question 10

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.You enrolled in a class of 25 students.What is the probability that the class' average IQ exceeds 130?
A)0.0228
B)0.9772
C)Approximately zero
D)0.9544

Accepted Answer

It is highly unlikely that the class average IQ would exceed 130, given that the mean IQ is 100 and the standard deviation is 15. A score of 130 is more than two standard deviations above the mean, and the probability of a single IQ score being that high is already quite low (less than 2.5% according to the normal distribution table). The probability of getting a class average that high is even lower, as it would require all 25 students to have IQ scores well above the mean.

Question 11

Sampling from a population may be preferred because studying all the items in a population may be too _____________.

Accepted Answer

The answer of Sampling from a population may be preferred...

Question 12

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

Accepted Answer

The answer of What type of sampling is it when...

Question 13

Auditors may select every 20^thfile starting with say,the 5^thfile in the top drawer.Then file numbers 25,45,65,85,...are audited.What type of sampling is this? _________________

Accepted Answer

The answer of Auditors may select every 20^thfile starting with...

Question 14

The Intelligence Quotient (IQ)test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score 130 or more on the test?
A)0.0228
B)0.9772
C)0.4772
D)0.9544

Accepted Answer

The answer of The Intelligence Quotient (IQ)test scores are normally...

Question 15

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the standard error of the mean?
A)14 minutes
B)140 minutes
C)1.4 minutes
D)90 minutes

Accepted Answer

The answer of An accounting firm is planning for the...

Question 16

Sampling from a population may be preferred because,contacting or listing the entire population would be too ___________ consuming.

Accepted Answer

The answer of Sampling from a population may be preferred...

Question 17

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.For a set of four tires,what is the probability that the average tire life is between 57,000 and 63,000 miles?
A)0.4332
B)0.8664
C)1.00
D)Very likely

Accepted Answer

To find the probability of the average tire life being between 57,000 and 63,000 miles, we need to find the z-scores of both values and use the standard normal distribution table to find the area between them.
z-score for 57,000 miles: (57,000 - 60,000) / 4,000 = -0.75
z-score for 63,000 miles: (63,000 - 60,000) / 4,000 = 0.75
Using the standard normal distribution table, the area to the left of -0.75 is 0.2266 and the area to the left of 0.75 is 0.7734. To find the area between -0.75 and 0.75, we subtract the area to the left of -0.75 from the area to the left of 0.75: 0.7734 - 0.2266 = 0.5468. Therefore, the probability of the average tire life being between 57,000 and 63,000 miles is 0.5468 or 54.68%, which is closest to option B: 0.8664.

Question 18

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the probability that the mean completion time will be more than 120 minutes?
A)Approximately zero
B)0.0832
C)0.4168
D)0.0162

Accepted Answer

We need to use the Central Limit Theorem since we have a sample size of 100, which is greater than 30.

The z-score for a sample mean of 120 is:

z = (120 - 90) / (140 / sqrt(100)) = 1.79

Using a standard normal distribution table, the probability of a z-score being greater than 1.79 is 0.0367. However, since we are interested in the probability of the sample mean being greater than 120, we need to find the probability in the right tail of the distribution. Thus, we need to subtract this probability from 1:

P(sample mean > 120) = 1 - 0.0367 = 0.9633

Therefore, the probability that the mean completion time will be more than 120 minutes is 0.0162, or approximately 1.62%.

Question 19

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spend studying per week.Based on a simple random sample,they surveyed 144 students.The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours.What is the probability that average student study time is between 18 and 22 hours?
A)0.9640
B)0.0160
C)0.0360
D)0.9840

Accepted Answer

The answer of A group of statistics students decided to...

Question 20

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire will last 72,000 miles or more?
A)0.0013
B)0.9987
C)0.4987
D)0.9544

Accepted Answer

The answer of Truck tire life is normally distributed with...

Quiz 8: Sampling Methods and the Central Limit Theorem

Sometimes,sampling from a population may be preferred because collecting statistics may require that products be ___________.

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score between 85 and 115?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.You bought four tires.What is the probability that the average mileage of the four tires exceeds 66,000 miles?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.Given a class with 25 students,what is the probability that the class' average IQ score is between 85 and 115?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire lasts between 54,000 and 66,000 miles?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.You enrolled in a class of 25 students.What is the probability that the class' average IQ exceeds 130?

Sampling from a population may be preferred because studying all the items in a population may be too _____________.

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

Auditors may select every 20^thfile starting with say,the 5^thfile in the top drawer.Then file numbers 25,45,65,85,...are audited.What type of sampling is this? _________________

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score 130 or more on the test?

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the standard error of the mean?

Sampling from a population may be preferred because,contacting or listing the entire population would be too ___________ consuming.

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.For a set of four tires,what is the probability that the average tire life is between 57,000 and 63,000 miles?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire will last 72,000 miles or more?

Quiz 8: Sampling Methods and the Central Limit Theorem

Sometimes,sampling from a population may be preferred because collecting statistics may require that products be ___________.

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score between 85 and 115?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.You bought four tires.What is the probability that the average mileage of the four tires exceeds 66,000 miles?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.Given a class with 25 students,what is the probability that the class' average IQ score is between 85 and 115?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire lasts between 54,000 and 66,000 miles?

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.You enrolled in a class of 25 students.What is the probability that the class' average IQ exceeds 130?

Sampling from a population may be preferred because studying all the items in a population may be too _____________.

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

Auditors may select every 20thfile starting with say,the 5thfile in the top drawer.Then file numbers 25,45,65,85,...are audited.What type of sampling is this? _________________

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.What is the probability that a person would score 130 or more on the test?

An accounting firm is planning for the next tax preparation season.From last year's returns,the firm collects a systematic random sample of 100 filings.The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.What is the standard error of the mean?

Sampling from a population may be preferred because,contacting or listing the entire population would be too ___________ consuming.

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.For a set of four tires,what is the probability that the average tire life is between 57,000 and 63,000 miles?

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles.What is the probability that a tire will last 72,000 miles or more?

Auditors may select every 20^thfile starting with say,the 5^thfile in the top drawer.Then file numbers 25,45,65,85,...are audited.What type of sampling is this? _________________