Exam 7: Introduction to Sampling Distributions

Given a population in which the probability of success is p = 0.20,if a sample of 500 items is taken,then calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23 if the sample size is 200.

Suppose it is known that the ages of all employees working for a very large computer company is normally distributed with a mean of 44.2 and a standard deviation of 5.6 years.Given this information,discuss what the sampling distribution for looks like?

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?

A sample of 25 observations is taken to estimate a population proportion π.The sampling distribution of sample proportion p is:

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 ounce.

The population mean of income for adults in a particular community is known to be $28,600.Given this information,the sampling distribution of values will be less than this depending on the size of the sample used in developing the sampling distribution.

If a population mean is equal to 200,the sample mean for a random sample selected from the population is about as likely to be higher or lower than 200.

A measure computed from the entire population is called:

Given a population where the proportion of items with a desired attribute is p = 0.25,if a sample of 400 is taken,what is the standard deviation of the sampling distribution of ?

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.

A population,with an unknown distribution,has a mean of 80 and a standard deviation of 7.For a sample of 49,the probability that the sample mean will be larger than 82 is:

Suppose a population is normally distributed with a mean 100 and a standard deviation of 15.When a sample of size n = 36 is collected a sampling distribution is created.Explain which is larger: the probability of a value randomly selected from the population being larger than 120,or the probability of a sample mean being larger than 120.

The annual income for independent sales representatives in the United States is thought to be highly right-skewed with a mean equal to $144,300 and a standard deviation of $32,450.Given this information,if a sample of 36 independent sales representatives is selected,what is the probability that the mean of the sample will exceed $130,000?

If a sample is selected using random sampling methods,the primary reason that the sample mean might be different from the corresponding population mean is that the sample might be biased.

A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P( ≤ 0.35).

According to an industry report,26 percent of all households have at least one cell phone.Further,of those that do have a cell phone,the mean monthly bill is $55.90 with a standard deviation equal to $9.60.Recently,a random sample of 400 households was selected.Of these households,88 indicated that they had cell phones.The mean bill for these 88 households was $57.00.What is the probability of getting 88 or fewer households with cell phones if the numbers provided by the industry report are correct?

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

A larger sample size reduces the potential for large sampling error.

The Central Limit Theorem is of most use to decision makers when the population is known to be normally distributed.

A local bank has 1,400 checking account customers.Of these,1,020 also have savings accounts.A sample of 400 checking account customers was selected from the bank of which 302 also had savings accounts.The sampling error in this situation is .0264.