7. How many different ways can the letters in “COUNT” be arranged? 8. How many different ways can the letters in “PROBABILITY” be arranged?

9. A pizza restaurant offers 15 different toppings, but only allows customers to select up to four different toppings for each pizza. How many different ways are there for customers to choose up to four toppings for a pizza?

10. A youth soccer team consists of 12 players. When they have games, they play simultaneously on two fields, so the team is divided into two groups of 6. How many ways can the 12 players be divided into two groups of six players if we only care which players are grouped together? Thanks!

Indicate if the following statements are true or false. For false statements, explain why the statement is false or give the correct answer.(1 point each)

6. A simple attribute can be broken down into smaller components.

7. The relationship between a weak and strong entity is called a multiple relationship.

8. An identifier is a combination of two or more attributes from two tables.

9. A unary relationship must have mandatory many cardinality on both sides.

10. If two entities are related many to many, we take the primary key of each entity and make it a foreign key in the other.

11. Compare and contrast overlap rule and disjoint rule. Compare and contrast total and partial specialization. (2.5+2.5=5 points total)

C program with functions

Make a dice game with the following characteristics:

must be two players with two dice.

when player 1 rolls the marker is annotated

when player 2 rolls the marker is annotated

in other words, for each roll the added scores must be shown.

Example:

Round 1:

player 1 score = 6

player 2 score = 8

Round 2:

player 1 score = 14

player 2 score = 20

Whoever reaches 35 points first wins.

if a player goes over 35 points, the last shot does not count, example:

If a player is at 30 points and when he rolls the two dice he gets 6 points, the sum (30 + 6) would be 36, it goes over 35 so that throw does not count and the score remains at 30.

Whoever gets double 3 or double 5 loses automatically.

3. Probability+ Central Limit Theorem questions:

a. The return on investment is normally distributed with a mean of 10% and a standard deviation of 5%. What is the probability of losing money?

b. An average male drinks 2 liter of water when active outdoor (with a standard deviation of 0.7). An organization is planning for a full day outdoor for 50 men and will bring 110 liter of water. What is the probability that the organization will run out of water? (8)

c. The lifetime of a certain battery is normally distributed with a mean of 10 hours and standard deviation of 1 hour. There are 4 such batteries in the package.

i. What is the probability that the lifetime of all 4 batteries exceed 11 hours?

ii. What is the probability that the total lifetime of all 4 batteries will exceed 44 hours.

A random sample of 8 drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums:

a. Make a scatter plot of the data

b. Calculate the correlation coefficient

c. Calculate a simple linear regression with Premium as the dependent variable and Experience as the independent variable

d. Is there a relationship between Driving Experience and Insurance Premium? Describe the relationship.

e. Predict the Monthly Auto Insurance Premium for a driver with 10 years of driving experience.

Suppose we have N = 6 values from a population. These values are 4, 8, 0, 10, 14 and 6. Let μ and σ denote the population mean and population standard deviation of these six values, respectively.

(a) What are the values of μ and σ, respectively?

μ = 4.8580; σ = 7

μ = 7; σ = 4.8580

μ = 7; σ = 4.4347

μ = 7; σ = 19.6667

μ = 7; σ = 23.6

(b) What percentage of the six population values stated above, fall within the interval (μ - σ, μ + σ) ?

66.66%

100%

50%

83.33%

16.66%

Consider a 42-ball lottery game. In total there are 42 balls numbered 1 through to 42 inclusive. Three balls are drawn (chosen randomly), one at a time, without replacement (so that a ball cannot be chosen more than once). To win the grand prize, a lottery player must have the same numbers selected as those that are drawn. The order of the numbers is not important so that if a lottery player has chosen the combination 20, 21, 22 and, in order, the numbers 21, 20, 22 are drawn, then the lottery player will win the grand prize (to be shared with other grand prize winners). You can assume that each ball has exactly the same chance of being drawn as each of the others.

(a) Consider the 42-ball lottery game described above. In how many different ways can you select a sample of three balls from a population of 42 balls?

1654895

14

105900

11480

42

(b) Consider the 42-ball lottery game described above. Recall that the order of the numbers chosen is not important and that each number can only be chosen once. In total, how many combinations are there available that include the numbers 20 and 21 but NOT the number 23?

40

14

42

3

39

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt concentration of 1 6 (1 + 1 4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation? (Round your answers to two decimal places.)

Consider the following project being analyzed for possible investment at ABC Corp. Initial Cost –$50 Inflow Year 1 $15 Inflow Year 2 $15 Inflow Year 3 $20 Inflow Year 4 $10 Inflow Year 5 $10 All amounts are in millions. The required return for the project is 8%. The project’s profitability index is: (Enter your answer out to two decimal places. As an example, you would enter 1.50 as 1.50)

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =