1. Suppose that the national average for the math portion of the College Board's SAT is 528. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places. If your answer is negative use “minus sign”.

1. We are interested in analyzing data related to football players for one season. Use T to denote the player is in their 30s and use F to denote a player plays offense. The probability that someone in their 30s in the data set is 10.2%. The probability that someone plays offense in the data set is 48.6%. The probability that someone is in their 30s and plays offense if 4.9%.
   1. What percentage of people in the NFL are in their 30s or play offense?
   2. What percentage of people in the NFL are in their 30s and do NOT play offense?
   3. Given someone is in their 30s, what is the probability that they play offense?
   4. What percentage of players are NOT in their 30s and are NOT on offense?
   5. Are T and F mutually exclusive events? Why or why not?
   6. Are T and F independent events? Explain, using probabilities.
   7. If we know someone plays offense, what is the probability they are in their 30s?

Suppose that the national average for the math portion of the College Board's SAT is 535. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 610? ______%

(b) What percentage of students have an SAT math score greater than 685?______ %

(c) What percentage of students have an SAT math score between 460 and 535?______ %

(d) What is the z-score for a student with an SAT math score of 630?

(e) What is the z-score for a student with an SAT math score of 395?

Acetaldehyde, CH3CHO, may be produced by the reaction of ethylene with oxygen in

the presence of a tetrachloropalladate catalyst according to the reaction:

2 CH2CH2+ O2? 2 CH3CHO

In an undesired side reaction some of the ethylene is oxidized to produce carbon

dioxide and water,

CH2CH2+ 3 O2? 2 CO2 + 2 H2O

A catalytic reactor is fed with a mixture of ethylene and oxygen only, and only the two

above reactions occur. The exit stream contains gas with the following composition:

CH2CH2 18.5 mol %

O2 unknown

CH3CHO 47.0 mol %

CO2 6.1 mol %

H2O unknown

Calculate:

a)The composition of the feed mixture.

b)The excess O2(expressed as a percentage).

c) The conversion of ethylene (expressed as a percentage).

d) The yield of acetaldehyde (expressed as a percentage).

e) The selectivity (expressed as a ratio).

For the following assume the results of an exam has a mean of 75 and a standard deviation of 5.

1. Calculate the percentage of students that score above 75.

2. Calculate the percentage of students that score below 65.

3. Calculate the percentage of students that score above 80.

4. The genius people in the class get a score in the top 1%. Calculate the score of the genius people.

5. Calculate the scores that you need to be between to be in the middle 80%.

6. Calculate the value of μ-2σ and μ+2σ. If a number is above μ+2σ it is considered an unusual value. If a number is below μ-2σ it is also considered an unusual value. These unusual values are also known as statistically significant. Determine if 83, 85, 87, 55, 64, 70, and 74 are statistically significant

Suppose that the national average for the math portion of the College Board's SAT is 516. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

Based on data from a college, scores on a certain test are normally distributed with a mean of 1530 and a standard deviation of 318. Find the percentage of scores greater than 2007, Find the percentage of scores less than 1053, Find the percentage of scores between 894-2166.

Table

8. a) Consider Bond C – a 4% coupon bond that has 10 years to maturity. It makes semi-annual payments and has a YTM of 7%. If interest rates suddenly drop by 2%, what is the percentage change of the bond? What does this problem tell you about the relationship between interest rate and bond price?

b) Consider another bond – Bond D, which is a 10% coupon bond. Similar to Bond C, it has 10 years to maturity. It also makes semi-annual payments and have a YTM of 7%. If interest rates suddenly drop by 2%, what is the percentage change of the bonds? Comparing the percentage change of bond C and bond D, what does this tell you about the interest rate risk of bonds with higher coupon rates?

1) Past research indicates that 64% of U.S. voters oppose capital punishment. A pollster wishes to estimate the current proportion of U.S. voters who oppose capital punishment to see if the percentage has changed.

a)How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to within 4%?b)Suppose they ignore the sample size found in part (a) and decide to select a random sample of 500 voters and find that 335 of them oppose capital punishment. Find and interpret a 95% confidence interval for the true percentage of U.S. voters who oppose capital punishment. Be sure to check the conditions and write them down!

c) Should the pollsters conclude that the percentage of current voters who oppose capital punishment has changed? Explain

Suppose that the national average for the math portion of the College Board's SAT is 531. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 631?

(b) What percentage of students have an SAT math score greater than 731?

(c) What percentage of students have an SAT math score between 431 and 531?

(d) What is the z-score for student with an SAT math score of 630?

(e) What is the z-score for a student with an SAT math score of 395?