The Easy Credit Company reports the following table representing a breakdown of costumers according to the amount the owe and whether a cash advance has been made. An auditor randomly selects one of the accounts. Amounts owed by the customers Cash Advance? Yes No $0 - $199.99 245 2890 $200 - $399.99 380 1700 $400 - $599.99 500 1425 $600 - $799.99 415 940 $800 - $999.99 260 480 $1000 or more 290 475 Total customers 2090 7910 What is the probability that a customer received a cash advance? What is the probability that a customer owed less than $200 and received a cash advance? What is the probability that a customer owed less than $200 or received a cash advance? Given that a customer received a cash advance, what is the probability that the customer owed $1000 or more? Given that a customer owed $1000 or more, what is the probability that the customer received a cash advance? Are the events “receiving a cash advance” and “owning $1000 or more” mutually exclusive? Explain using probabilities. Are the events “receiving a cash advance” and “owning $1000 or more” independent? Explain using probabilities. Many U.S. households still do not have Internet access. Suppose 25 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign, the company decides to randomly select ten households and offer them red laptops along with a brochure that describes their services. The aim is to build goodwill and, with a free laptop, tempt nonusers into getting Internet access. What is the probability that six laptop recipients do not have Internet access? What is the probability that at least five recipients do not have Internet access? What is the probability that two or fewer laptop recipients do not have Internet access? What is the expected number of laptop recipients who do not have Internet access? Calculate the expected value, the variance, and the standard deviation for the recipients who do not have Internet access. Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. What is the probability that a randomly selected household will have an income between $50,000 and $65,000? What is the probability that a randomly selected household will have an income of more than $70,000? What minimum income does a household need to earn to be in the top 5% of incomes? What maximum income does a household need to earn to be in the bottom 40% of incomes? The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008. Based on the 2006 compensation data obtained from the securities and exchange commission (SEC) website, it was determined that the mean and the standard deviation of the compensation for the 500 paid CEOs in publicly traded U.S. companies are $10.32 million and $9.78 million, respectively. An analyst randomly choses 32 CEO compensations for 2006. Is it necessary to apply the finite population correction factor? Explain. Is the sampling distribution of the sample mean approximately normally distributed? Explain. Calculate the expected value and the standard error of the sample mean. What is the probability that the sample mean is more than $12 million? What is the probability that the sample mean is between $10 million to $12 million?

The Easy Credit Company reports the following table representing a breakdown of costumers according to the amount the owe and whether a cash advance has been made. An auditor randomly selects one of the accounts. Amounts owed by the customers Cash Advance? Yes No $0 - $199.99 245 2890 $200 - $399.99 380 1700 $400 - $599.99 500 1425 $600 - $799.99 415 940 $800 - $999.99 260 480 $1000 or more 290 475 Total customers 2090 7910 What is the probability that a customer received a cash advance? What is the probability that a customer owed less than $200 and received a cash advance? What is the probability that a customer owed less than $200 or received a cash advance? Given that a customer received a cash advance, what is the probability that the customer owed $1000 or more? Given that a customer owed $1000 or more, what is the probability that the customer received a cash advance? Are the events “receiving a cash advance” and “owning $1000 or more” mutually exclusive? Explain using probabilities. Are the events “receiving a cash advance” and “owning $1000 or more” independent? Explain using probabilities. Many U.S. households still do not have Internet access. Suppose 25 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign, the company decides to randomly select ten households and offer them red laptops along with a brochure that describes their services. The aim is to build goodwill and, with a free laptop, tempt nonusers into getting Internet access. What is the probability that six laptop recipients do not have Internet access? What is the probability that at least five recipients do not have Internet access? What is the probability that two or fewer laptop recipients do not have Internet access? What is the expected number of laptop recipients who do not have Internet access? Calculate the expected value, the variance, and the standard deviation for the recipients who do not have Internet access. Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. What is the probability that a randomly selected household will have an income between $50,000 and $65,000? What is the probability that a randomly selected household will have an income of more than $70,000? What minimum income does a household need to earn to be in the top 5% of incomes? What maximum income does a household need to earn to be in the bottom 40% of incomes? The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008. Based on the 2006 compensation data obtained from the securities and exchange commission (SEC) website, it was determined that the mean and the standard deviation of the compensation for the 500 paid CEOs in publicly traded U.S. companies are $10.32 million and $9.78 million, respectively. An analyst randomly choses 32 CEO compensations for 2006. Is it necessary to apply the finite population correction factor? Explain. Is the sampling distribution of the sample mean approximately normally distributed? Explain. Calculate the expected value and the standard error of the sample mean. What is the probability that the sample mean is more than $12 million? What is the probability that the sample mean is between $10 million to $12 million?

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Author:Amos Gilat

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Amounts owed by the customers	Cash Advance?
Yes	No
$0 - $199.99	245	2890
$200 - $399.99	380	1700
$400 - $599.99	500	1425
$600 - $799.99	415	940
$800 - $999.99	260	480
$1000 or more	290	475
Total customers	2090	7910

What is the probability that a customer received a cash advance?
What is the probability that a customer owed less than $200 and received a cash advance?
What is the probability that a customer owed less than $200 or received a cash advance?
Given that a customer received a cash advance, what is the probability that the customer owed $1000 or more?
Given that a customer owed $1000 or more, what is the probability that the customer received a cash advance?
Are the events “receiving a cash advance” and “owning $1000 or more” mutually exclusive? Explain using probabilities.
Are the events “receiving a cash advance” and “owning $1000 or more” independent? Explain using probabilities.

Many U.S. households still do not have Internet access. Suppose 25 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign, the company decides to randomly select ten households and offer them red laptops along with a brochure that describes their services. The aim is to build goodwill and, with a free laptop, tempt nonusers into getting Internet access.

What is the probability that six laptop recipients do not have Internet access?
What is the probability that at least five recipients do not have Internet access?
What is the probability that two or fewer laptop recipients do not have Internet access?
What is the expected number of laptop recipients who do not have Internet access?
Calculate the expected value, the variance, and the standard deviation for the recipients who do not have Internet access.

Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500.

What is the probability that a randomly selected household will have an income between $50,000 and $65,000?
What is the probability that a randomly selected household will have an income of more than $70,000?
What minimum income does a household need to earn to be in the top 5% of incomes?
What maximum income does a household need to earn to be in the bottom 40% of incomes?

The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008. Based on the 2006 compensation data obtained from the securities and exchange commission (SEC) website, it was determined that the mean and the standard deviation of the compensation for the 500 paid CEOs in publicly traded U.S. companies are $10.32 million and $9.78 million, respectively. An analyst randomly choses 32 CEO compensations for 2006.

Is it necessary to apply the finite population correction factor? Explain.
Is the sampling distribution of the sample mean approximately normally distributed? Explain.
Calculate the expected value and the standard error of the sample mean.
What is the probability that the sample mean is more than $12 million?
What is the probability that the sample mean is between $10 million to $12 million?

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