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Business Statistics_CH 6 and 7
Chapter 6 and 7 take-home exam
50
Business
Undergraduate 3
03/30/2010

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Cards

Term
False
Definition
True/False: the normal dist. is one of the most frequently used discrete prob. dist.
Term
True
Definition
True/False: typically a continuous random variable is one whose value is determined by measurement instead of counting.
Term
False
Definition

True/False:

All symmetric distributions can be assumed normally distributed.

Term
True
Definition

True/False: The number of defects manufactured by workers in a small engine plant is an example of a discrete random variable.

Term
False
Definition

True/False: A continuous random variable approaches normality as the level of skewness increases.

Term
True
Definition

True/False: The parameters of a normal distribution are the mean and the standard deviation.

Term
False
Definition

True/False: If the mean, median and mode are all equal for a continuous random variable, then the random variable is normally distributed.

Term
0.1131
Definition

Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?

Term
Approximately 0.6534
Definition

The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a standard deviation equal to $80. Based on this information, what are the chances that the revenue on the first show will be between $300 and $500?

Term
About 11.23 min.
Definition

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. The manager has decided to have a signal system attached to the phone so that after a certain period of time, a sound will occur on her employees' phone if she exceeds the time limit. The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls. The time limit should be:

Term
0.0202
Definition

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course?

Term
Essentially Zero
Definition

The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. Based on this information, what are the chances that the revenue on the first show will exceed $800?

Term
about 0.0125
Definition

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes?

Term
Approximately 0.00001
Definition

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. What is the probability that three randomly monitored calls will each be completed in 4 minutes or less?

Term
Approx. 1.86 pounds
Definition

The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.

Term
Approx. 2.34 mpg
Definition

A major U.S. automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg. A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city. Given this information, what is the city mileage standard deviation for this SUV model?

Term
Approx. 0.29
Definition

A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours. Given this information, what is the probability that a deliberation will last between 10 and 15 hours?

Term
89.44 percent
Definition

Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent. What percent of investors at this brokerage hour earned at least 5 percent?

Term
About 13.6 percent
Definition

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of changing its fee structure so that anyone who uses the phone less than 250 minutes during a given month will pay a reduced monthly fee. Based on the available information, what percentage of current customers would be eligible for the reduced fee?

Term
about 237 minutes
Definition

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of charging a lower rate for customers who use the phone less than a specified amount. If they wish to give the rate reduction to no more than 12 percent of their customers, what should the cut-off be?

Term
True
Definition
True/False: The size of the sampling error that comes from a random sample depends on both the variation in the population and the size of the sample being selected.
Term
True
Definition
True/False: Sampling error is the difference between the population parameter and the sample statistic.
Term
False
Definition
True/False: the sample mean is a parameter
Term
False
Definition

True/False: Taking a larger sample size will always result in less sampling error but costs more money and takes more time.

Term
True
Definition

True/False: The actual mean fill volume for all bottles of a soft drink product that were filled on a Tuesday is 11.998 ounces. A sample of 64 bottles was randomly selected and the sample mean fill volume was 12.004 ounces. Based upon this information, the sampling error is .006 ounces.

Term
False
Definition

True/False: Suppose it is known that the mean purchase price for all homes sold last year in Blacksburg, Virginia was $203,455. Recently, two studies were done on home sales prices. In the first study, a random sample of 200 homes was selected from the population. In the second study, a random sample of 60 homes was selected. Based on this information, we know that the second study would contain more sampling errors than the first study due to the smaller sample size.

Term
True
Definition
True/False: an increase in sample size will tend to result in less sampling error
Term
False
Definition
True/False: a sampling dist. is the dist. of the individual values that are included in a sample from a population.
Term
True.
Definition
True/False: a sampling dist. for a sample mean shows the dist. of the possible values for the sample mean for a given sample size from a population.
Term
True
Definition

True/False: Although the concept of sampling distributions is an important concept in statistics, it is very unlikely that a decision maker will actually construct a sampling distribution in any practical business situation.

Term
True
Definition

True/False: The mean of a sampling distribution would be equal to the mean of the population from which the sampling distribution is constructed.

Term
True
Definition

True/False:

If a population is normally distributed, then the sampling distribution for the sample mean will always be normally distributed regardless of the sample size.

Term
False
Definition

True/False:

If a population is not normally distributed, then the sampling distribution for the mean also cannot be normally distributed.

Term
True
Definition

True/False:

The size of the standard error of the sample proportion is dependent on the value of the population proportion and the closer the population proportion is to .50, the larger the standard error for a given sample size will be.

Term
likely be different from the population mean.
Definition
When sampling from a population , the sample mean will
Term
-0.55 percent
Definition

The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city:

6.9

7.5

6.5

7

7.3

6.8

6.5

7

7

7.2

7.5

7.8

6

7


Given this information, what is the most extreme amount of sampling error possible if a random sample of n = 4 banks is surveyed and the mean loan rate is calculated?

Term
Approx. -0.07
Definition

The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city:

6.9

7.5

6.5

7

7.3

6.8

6.5

7

7

7.2

7.5

7.8

6

7


Given this information, what would the sampling error be if a sample including the seven values in the top row were used to compute the sample mean?

Term
The potential for extreme sampling error is reduced
Definition
The impact on sampling of increasing the sample size is..
Term
2.5
Definition

A particular subdivision has 20 homes. The number of people living in each of these homes is listed as follows:

2

4

7

3

4

2

4

5

2

3

5

4

6

3

4

2

2

1

4

3


If a random sample of n = 3 homes were selected, what would be the highest possible positive sampling error?

Term
About $195.00
Definition

If the monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00, which of the following would be the largest individual customer bill that you might expect to find?

Term
80
Definition

The Olsen Agricultural Company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds. Based on this, what is the mean of the sampling distribution for  x bar if the sample size is n=64?

Term
0.9544
Definition

The Olsen Agricultural Company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds. Based on this, what is the probability that the mean weight of the bales in a sample of n=64 bales will be between 78 and 82 pounds?

Term
0.3821
Definition

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons. Based on this information, if the department employee selects a random sample of n=9 containers, what is the probability that the mean volume for the sample will be greater than 1.01 gallons?

Term
About 0.1841
Definition

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons. The department's test process requires that they select a random sample of n=9 containers. If the sample mean is less than 0.97 gallons, the department will fine the dairy. Based on this information, what is the probability that the dairy will get fined even when its filling process is working correctly?

Term
C
Definition

Suppose it is known that the income distribution in a particular region is right-skewed and bi-modal. If bank economists are interested in estimating the mean income, which of the following is true?

A-The sampling distribution will be left-skewed.

 

B-The sampling distribution will also be right-skewed for large sample sizes.

 

C-Provided that the sample size is sufficiently large, the sampling distribution for  x bar will be approximately normal with a mean equal to the population mean that they wish to estimate.

 

D- The standard deviation of the sampling distribution for x bar will be proportionally larger than the population standard deviation, depending on the size of the sample.

 
Term
Approx 0.0351
Definition

A golf course in California has determined that the mean time it takes for a foursome to complete an 18 hole round of golf is 4 hours 35 minutes (275 minutes) with a standard deviation of 14 minutes. The time distribution is also thought to be approximately normal. Every month, the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play. Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes). What is the probability of seeing a sample mean this high or higher?

Term
0.1587
Definition

The J.R. Simplot Company produces frozen French fries that are then sold to customers such as McDonald's. The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inches. To make sure that Simplot continues to meet the quality standard for "prime" fries, they plan to select a random sample of n = 100 fries each day. Yesterday, the sample mean was 6.05 inches. What is the probability that the mean would be 6.05 inches or more if they are meeting the quality standards?

Term
0.0023
Definition

The St. Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inches. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 2.9 inches?

Term
0.0014
Definition

A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. Suppose that the company selects a random sample of 400 pages and finds 33 that have an error. If the printer is meeting the standard, what is the probability that a sample would have 33 or more errors?

Term
about 0.0838
Definition

A pharmaceutical company claims that only 5% of patients experience nausea when they take a particular drug. In a research study n = 100 patients were given this drug and 8 experienced nausea. Assuming that the company's claim is true, what is the probability of 8 or more patients experiencing nausea?

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