1. Consider a bank that has the following assets and liabilities:

• Loans of $100 million with a realized rate of 5%
• Security holdings of $50 million earning 10% interest income
• Reserves of $10 million
• Savings accounts of $100 million interest of 2.5%
• Checking deposits of $30 million which pay no interest

1. Determine the profits for this bank. (Hint: The bank earns income, or revenues, not only from its loans but also from any securities it holds!)

1) The IQ of the author’s college students is normally distributed with a mean of 100 and a standard deviation of 15. What percentage of college students have IQs between 70 to 130? (Use the empirical rule to solve the problem) Please explain how you get the answer. You can use excel to show how to use the formula if needed.

2) At a high school, GPA’s are normally distributed with a mean of 2.6 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.1 and 3.1? Please explain how you get the answer. You can use excel to show how to use the formula if needed.

Assume that IQ scores are normally distributed with a mean of 100 and standard deviation of 12. Find the probability that: (a) a randomly selected person has an IQ score less than 92. (b) a randomly selected person has an IQ score greater than 108.

IQ scores are known to be normally distributed. The mean IQ score is 100 and the standard deviation is 15. What percent of the population has an IQ between 85 and 105. Need to solve it through Excel

What is the future value of $100 deposited in an account for four years paying a 6 percent annual rate of interest, compounded semiannually?

What is the future value of an ordinary annuity of $2,000 each year for 10 years, invested at 12 percent?

Gina has planned to start her college education four years from now. To pay for her college education, she has decided to save $1,000 a quarter for the next four years in an investment account expected to yield 12 percent. How much will she have at the end of the fourth year? (Assume quarterly compounding.)

What is the future value of $100 deposited in an account for four years paying a 6 percent annual rate of interest, compounded semiannually?

What is the future value of an ordinary annuity of $2,000 each year for 10 years, invested at 12 percent?

Gina has planned to start her college education four years from now. To pay for her college education, she has decided to save $1,000 a quarter for the next four years in an investment account expected to yield 12 percent. How much will she have at the end of the fourth year? (Assume quarterly compounding.)

1. A sample of 100 results in 27 successes.
a. Calculate the point estimate for the population proportion of successes. (Do not round intermediate calculations. Round your answer to 3 decimal places.)  

b. Construct 95% and 90% confidence intervals for the population proportion. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

95% -

90%-

c. Can we conclude at 95% confidence that the population proportion differs from 0.330?  

• No, since the confidence interval does not contain the value 0.330.

• No, since the confidence interval contains the value 0.330.

• Yes, since the confidence interval does not contain the value 0.330.

• Yes, since the confidence interval contains the value 0.330.

d. Can we conclude at 90% confidence that the population proportion differs from 0.330?

• No, since the confidence interval contains the value 0.330.

• No, since the confidence interval does not contain the value 0.330.

• Yes, since the confidence interval contains the value 0.330.

• Yes, since the confidence interval does not contain the value 0.330.

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..0200

B..0500

C..0228

D..0250

What is the probability that a person would score between 85 and 115?

A..6826

B..6800

C..3413

D..6587

Suppose that you enrolled in a class of 36 students, what is the probability that the class’ average IQ exceeds 130?

A.

almost zero

B.

.0250

C.

.0500

D.

.2280

What is the probability that a person would score between 115 and 130?

In a large population, 46% of the households own VCR’s. A SRS of 100 households is to be contacted and asked if they own a VCR.

a. Let p^ be the sample proportion who say they own a VCR. find the mean of the sampling distribution of the sample proportion

b. Let p^ be the sample proportion who say they own a VCR. Find the standard deviation of the sampling distribution of the sample proportion

c. Let p^ be the sample proportion who say they own a VCR. Why is the sampling distribution of p^ approximately normal

d. What is the probability that more than 60 will own VCRs?

e. Let p^ be the sample proportion who say they own a VCR. If we decrease the sample size from 100 to 50 that would multiply the standard deviation of the sampling distribution by a factor of:

The Ultimatum Game: A and B are two individuals who are to divide $100. A (chosen randomly by a coin toss) makes an offer to B. There is a minimum offer of $10. Assume, for simplicity, that offers must be evenly divisible by 10 (i.e., A can offer $10, or $20, or $30 etc.) B can either accept or reject the offer. If B accepts, they split the $100 as per the amount offered. For example, if A offers $20, and B accepts, then B gets $20 and A gets $80. Both players have full knowledge of the payoffs and rules of the game. If B rejects, both get nothing and the game ends. Assume that A and B have never met before and will never meet or play this game again, and both know it. Suppose you won the coin toss and you are A. Answer the following: What offer do you make? Why? What did you assume about B's motivation(s)?

Comment on the implications of assuming rational self-interest as the most important motivator for economic choices.