True or False: Of the major economies in the world, the United States had the highest growth rate of real GDP per capita between 1982 and 2009.

・True

・False

Japan experienced average annual real GDP per capita growth of 2.0% between 1982 and 2009. Which of the following helped most to contribute to that growth?

・Redistributive policies designed to decrease poverty

・Privatization of previously nationalized industries

・Spending on research and development

Argue analytically that a completely impure node yields the highest Gini Impurity.

Using the data in the following array write a program that finds and outputs the highest value, the lowest value, the count of elements in the array, the average value in the array, and the mode - the value that appears most often.

dataArray = {173.4, 873.7, 783.9. 000.0, -383.5, 229.5, -345.5, 645.5, 873.7, 591.2};

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for a season.

ta. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Enter negative value as negative number.

Win % = _______+_________*Yds/At

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

Win % = _______+_________*Yds/Att

c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

Win % = _______+_________*Yds/Att+______*Int/Att

d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

Predicted Percentage _________ (<, >, =) Actual Percentage ___________

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of  NFL teams for a season

a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Enter negative value as negative number.

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

d. The average number of passing yards per attempt for the Kansas City Chiefs was  and the number of interceptions thrown per attempt was . Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was  wins and  losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for a season

a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Enter negative value as negative number.

Win%= ----------- + ---------. Yds/Att

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

Win%= ----------- + ---------. Int/Att

c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

Win%= ----------- + ---------. Yds/Att + ---------. Int/Att

d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of  NFL teams for a season

a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Enter negative value as negative number.

WIN%=______+_______*Yds/Att

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

      WIN%=______+_______*INT/Att

c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Enter negative value as negative number.

        WIN%=______+_______*Yds/Att+______*INT/Att

d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036 . Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

People who hack into computer systems or use someone else’s bank card, through trial and error, will try to figure out the PIN (personal identification number) or password by using personal information. Because PIN numbers must be easily remembered by the person who uses one of these security devices, people often rearrange numbers or letters that are significant to them and use them as a password or PIN. For instance, someone may use the numbers in their birth date as a PIN number. Some will use initials or an important word in their passwords. Answer the following questions about a person who uses significant personal information for their PIN number.

1. If a PIN must be exactly four numbers long, how many possible PIN numbers could a person use?
2. A person decides to use numbers from their date of birth and year of birth in their PIN:

13th of August, 1987

If they use the numbers 13 and 87 in their PIN, how many different PINs could they have? List all the possible PIN numbers by using a tree diagram to organize your counting. The tree diagram has been started for you, but you must complete it.

Be careful. In this situation, each of the numbers will be used only once.

3. Say for instance this person’s PIN is 1387. If a hacker does not know your birth date or does not use your birthday, what is the probability that the hacker will obtain your PIN by chance?
4. If the hacker does know your birth date and decides to use these numbers in various combinations to find your PIN, what is the probability that the hacker will find out your PIN on the first try?
5. What if the person used the month and the year of his/her birth, specifically: 08 for the month and 87 for the year. How many different possible PINs could be used? Use a tree diagram to determine all the possible PINs so that each number is used once, except 8 that must be used twice.
6. If the person’s PIN is 8078, but the hacker does not know any of this information, what is the probability that they will obtain the PIN on the first try?
7. If the hacker does know the birth information and uses these four numbers, what is the probability that the hacker will obtain the PIN on the first try?
8. What do you conclude about the use of personal information to make up the numbers in a PIN? Describe how the knowledge of probability is useful in deciding on a PIN and in protecting personal information through the use of these PINs.

The age distribution of students at a community college is given below.

Age (years) Number of Students (f)

Under 21 416

21-25 420

26-30 219

31-35 51

Over 35 24

Total = 1130

Number of students (f) 416 420 219 51 24 1130

A student from the community college is selected at random. Find the conditional probability that the student is at most 35 given that he or she is at least 26.

The quality of new Ferrari cars is assessed by sending each new car through a certifier who examines every part of the car’s interior and exterior for defects and counts the number of defects. The number of defects averages 0.1 per car.

Note: Make sure to specify the random variables and their distributions. Use the appropriate cumulative distribution tables to compute the probabilities.

(a) Find the probability the next inspected car will have more than 1 defects. (5 pts.)