Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage and three-point field goal percentage. The data are stored in NBA.xlsx

1) At the 0.05 level of significance, perform a F test to determine whether the regression model has any significant variable. Use p-value to explain.

Specialized discrete probability distributions are useful for specific applications. Discuss the concepts of a random variable and a probability distribution. Discuss discrete probability distributions that are often used in business applications. Provide examples.

Work for the first variable, X:

2. Construct a frequency table, containing at least 5 classes, but no more than 8 classes. [2]

**Data goes up to 83**

3. Make the following graphs, using Stat Crunch.

1. histogram [2]

2. frequency polygon [2]

3. cumulative frequency polygon [2]

4. stem and leaf [2]

5. box plot [2]

Work for the first variable, X:

2. Construct a frequency table, containing at least 5 classes, but no more than 8 classes. [2]

3. Make the following graphs, using Stat Crunch.

1. histogram [2]

2. frequency polygon [2]

3. cumulative frequency polygon [2]

4. stem and leaf [2]

5. box plot [2]

4. Obtain the descriptive statistics. [1]

Adrian and Bobby play on opposing basketball teams. Bobby is always assigned to defend against Adrian. At the start of a game, Adrian feels confident with probability 3/4, and independently Bobby feels aggressive with probability 2/3. Adrian will take 20 shots at the basket if feeling confident, but only 12 if not. When Bobby is aggressive, Adrian scores on each shot with independent probability .4; otherwise Adrian’s probability of scoring is .6. Given that Adrian scored 10 times, what is the probability that Bobby was aggressive?

Student scores on Professor Combs' Stats final exam are normally distributed with a mean of 72 and a standard deviation of 7.5

Find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one student chosen at random scores above an 77.  

b.) The probability that 20 students chosen at random have a mean score above an 77.  

c.) The probability that one student chosen at random scores between a 67 and an 77.  

d.) The probability that 20 students chosen at random have a mean score between a 67 and an 77.

Discuss a probability model by 1. stating a sample space and assigning probabilities to outcomes in the space. 2. Is the model discrete or continuous? 3. Can you verify that it satisfies the rules of probability? 4. Can you identify any events that are independent, or any that are dependent? 5. Can you identify any events whose probability would require the inclusion-exclusion principle to calculate? 6. Can you identify any events whose probability would require conditional probability to calculate? Find these probabilities if possible.

When coin 1 is flipped, it lands on heads with probability   3 /5  ; when coin 2 is flipped it lands on heads with probability   7 /10  .

(a) If coin 1 is flipped 9 times, find the probability that it lands on heads at least 7 times.

(b) If one of the coins is randomly selected and flipped 8 times, what is the probability that it lands on heads exactly 5 times?

(c) In part (b), given that the first of these 8 flips lands on heads, find the conditional probability that exactly 5 of the 8 flips land on heads.