Exam 8: Sampling Distributions

A firm claims that only 10% of its accounts receivables are over 30 days past due.The bank that supplies working capital or interim loans to the firm is suspect of the figure and accordingly takes a random sample of 100 accounts of the firm.Find the probability that the sample proportion,p,will be: A)between 9 and 10%. B)within 2% points of the true proportion.

(Short Answer)

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Question 81

The sampling distribution of the mean will be approximately normal regardless of the distribution of the original population or the sample size.

(True/False)

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Question 82

The chairman of a statistics department in a certain college believes that 70% of the department's graduate assistantships are given to international students.A random sample of 50 graduate assistants is taken.Assume that the chairman is correct and that $\pi$ = 0.70.What is the probability that the sample proportion p will be between 0.65 and 0.73?

(Short Answer)

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Question 83

The average cost of renting a compact size car in a major metropolitan area of the U.S.is $51.74 with a standard deviation of $7.48.Assume a normal distribution.If a sample of 20 cities is taken,what is the probability that the sample mean will fall between 47.74 and 55.74?

(Short Answer)

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Question 84

A Poisson probability distribution with a mean of 4 must have a standard deviation of ____________________.

(Short Answer)

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Question 85

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

(True/False)

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Question 86

When a great many simple random samples of size n are drawn from a population that is normally distributed,the sampling distribution of the sample means will be regardless of sample size n.As n increases,the of the sample distribution will become smaller.

(Short Answer)

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Question 87

For each of the following combinations of n and $\pi$ ,calculate the mean of the sampling distribution of the sample proportion p. A)n = 100; $\pi$ = 0.38 B)n = 200; $\pi$ = 0.92 C)n = 2000; $\pi$ = 0.02

(Short Answer)

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Question 88

In a simple random sample of 1,000 automobile owners between ages 25-35,there were 142 owners of a Ford Explorer.If the expected number of owners of this vehicle was 125 out of 1000,the values of $\pi$ p,and n are,respectively:

(Multiple Choice)

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Question 89

The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that a randomly selected American adult plays sports for more than 5 hours per day.

(Short Answer)

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Question 90

The Central Limit Theorem states that the sampling distribution of the mean will be approximately normal provided that the sample size is greater than 30.

(True/False)

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Question 91

If all possible samples of size n are drawn from an infinite population with a mean of $\mu$ and a standard deviation of $\text { ? }$ ,then the standard error of the sample mean is inversely proportional to:

(Multiple Choice)

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Question 92

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1070?

(Short Answer)

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Question 93

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed less than 195 pages with one cartridge?

(Short Answer)

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Question 94

The Coca-Cola Company has 40% of the cola market.Determine the probability that a sample proportion for n = 30 is within 0.10 of the true proportion of 0.40,which is the proportion of cola drinkers who prefer a Coca-Cola drink.In this particular market,the population size of those who drink cola is 50.

(Multiple Choice)

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Question 95

Pets Name = Number of Pets Abby 2 Brenda 1 Caro1 3 David 4 Ed 2 -Determine the probability distribution for the discrete random variable,x = number of pets owned.

(Essay)

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Question 96

Your company is located in New York City and your job requires that you travel by air to many other major cities such as Boston,Chicago,Los Angeles,Detroit,Houston,Dallas,Atlanta,Denver,and Washington,DC.Your average round-trip airfare for the past year has been $495 with a standard deviation of $240.If for your next year's planning budget you estimate your average air ticket between $395 and $550,what is the probability that the mean, $\bar { x }$ ,of your next 36 flights will fall in this range?

(Short Answer)

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Question 97

In a production of 1000 plastic moldings,75 were incompletely formed and had to be discarded.Based on these data the total production of plastic moldings should have what estimated proportion of incompletely formed moldings?

(Short Answer)

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Question 98

A manufacturer of printers claims that their color cartridge will print an average of 200 4-by-6 photos with a standard deviation of 60 photos.A random sample of 40 customers counted the number of photos printed with one cartridge.If the manufacturer's claim is correct,what is the probability that the average customer printed between 190 and 205 pages with one cartridge?

(Short Answer)

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Question 99

Sixty percent of a company's customers are females.What is the probability that a random sample of 200 customers is greater than 64 percent female?

(Multiple Choice)

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Question 100

Showing 81 - 100 of 108

The sampling distribution of the mean will be approximately normal regardless of the distribution of the original population or the sample size.

The average cost of renting a compact size car in a major metropolitan area of the U.S.is $51.74 with a standard deviation of $7.48.Assume a normal distribution.If a sample of 20 cities is taken,what is the probability that the sample mean will fall between 47.74 and 55.74?

A Poisson probability distribution with a mean of 4 must have a standard deviation of ____________________.

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

When a great many simple random samples of size n are drawn from a population that is normally distributed,the sampling distribution of the sample means will be regardless of sample size n.As n increases,the of the sample distribution will become smaller.

For each of the following combinations of n and $\pi$ ,calculate the mean of the sampling distribution of the sample proportion p. A)n = 100; $\pi$ = 0.38 B)n = 200; $\pi$ = 0.92 C)n = 2000; $\pi$ = 0.02

In a simple random sample of 1,000 automobile owners between ages 25-35,there were 142 owners of a Ford Explorer.If the expected number of owners of this vehicle was 125 out of 1000,the values of $\pi$ p,and n are,respectively:

The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that a randomly selected American adult plays sports for more than 5 hours per day.

The Central Limit Theorem states that the sampling distribution of the mean will be approximately normal provided that the sample size is greater than 30.

If all possible samples of size n are drawn from an infinite population with a mean of $\mu$ and a standard deviation of $\text { ? }$ ,then the standard error of the sample mean is inversely proportional to:

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1070?

Pets Name = Number of Pets Abby 2 Brenda 1 Caro1 3 David 4 Ed 2 -Determine the probability distribution for the discrete random variable,x = number of pets owned.

In a production of 1000 plastic moldings,75 were incompletely formed and had to be discarded.Based on these data the total production of plastic moldings should have what estimated proportion of incompletely formed moldings?

Sixty percent of a company's customers are females.What is the probability that a random sample of 200 customers is greater than 64 percent female?

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Exam 8: Sampling Distributions

The sampling distribution of the mean will be approximately normal regardless of the distribution of the original population or the sample size.

The average cost of renting a compact size car in a major metropolitan area of the U.S.is $51.74 with a standard deviation of $7.48.Assume a normal distribution.If a sample of 20 cities is taken,what is the probability that the sample mean will fall between 47.74 and 55.74?

A Poisson probability distribution with a mean of 4 must have a standard deviation of ____________________.

The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

When a great many simple random samples of size n are drawn from a population that is normally distributed,the sampling distribution of the sample means will be ____________________ regardless of sample size n.As n increases,the ____________________ of the sample distribution will become smaller.

For each of the following combinations of n and π\piπ ,calculate the mean of the sampling distribution of the sample proportion p. A)n = 100; π\piπ = 0.38 B)n = 200; π\piπ = 0.92 C)n = 2000; π\piπ = 0.02

In a simple random sample of 1,000 automobile owners between ages 25-35,there were 142 owners of a Ford Explorer.If the expected number of owners of this vehicle was 125 out of 1000,the values of π\piπ p,and n are,respectively:

The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that a randomly selected American adult plays sports for more than 5 hours per day.

The Central Limit Theorem states that the sampling distribution of the mean will be approximately normal provided that the sample size is greater than 30.

If all possible samples of size n are drawn from an infinite population with a mean of μ\muμ and a standard deviation of ? \text { ? } ? ,then the standard error of the sample mean is inversely proportional to:

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1070?

Pets Name = Number of Pets Abby 2 Brenda 1 Caro1 3 David 4 Ed 2 -Determine the probability distribution for the discrete random variable,x = number of pets owned.

In a production of 1000 plastic moldings,75 were incompletely formed and had to be discarded.Based on these data the total production of plastic moldings should have what estimated proportion of incompletely formed moldings?

Sixty percent of a company's customers are females.What is the probability that a random sample of 200 customers is greater than 64 percent female?

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

When a great many simple random samples of size n are drawn from a population that is normally distributed,the sampling distribution of the sample means will be regardless of sample size n.As n increases,the of the sample distribution will become smaller.

For each of the following combinations of n and $\pi$ ,calculate the mean of the sampling distribution of the sample proportion p. A)n = 100; $\pi$ = 0.38 B)n = 200; $\pi$ = 0.92 C)n = 2000; $\pi$ = 0.02

In a simple random sample of 1,000 automobile owners between ages 25-35,there were 142 owners of a Ford Explorer.If the expected number of owners of this vehicle was 125 out of 1000,the values of $\pi$ p,and n are,respectively:

If all possible samples of size n are drawn from an infinite population with a mean of $\mu$ and a standard deviation of $\text { ? }$ ,then the standard error of the sample mean is inversely proportional to: