Work Exercises 1 and 2 using the formula for the probability density function and a hand calculator. Do not use EXCEL. Show all of your work.

1. Assume 45% of all persons three years of age and older wear glasses or contact lenses, For a randomly selected group of seven people, what is the probability that
   1. Exactly 3 wear glasses or contact lenses?
   2. At least 3 wear glasses or contact lenses?
   3. At most 5 wear glasses or contact lenses?
   4. Between 2 and 6 wear glasses or contact lenses?

2. Assume 75% of youths 12-17 years of age have a systolic blood pressure less than 136 mm of mercury. What is the probability that a sample of 12 youths of that age will include
   1. Exactly 8 who have systolic blood pressure less than 136?
   2. Less than 10 who have systolic blood pressure less than 136?
   3. At least 10 who have systolic blood pressure less than 136?
   4. Between 5 and 8 who have systolic blood pressure less than 136?

3. Use EXCEL to complete the entries in the following table. Assume
   1. X represents the number of current cigarette smokers in a sample of size 10.
   2. Each selected subject has a 25% of being a current cigarette smoker.
   3. Being a current cigarette smoker is independent for all subjects

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 13 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.36 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

lower limit:

upper limit:

margin of error:

(b) What conditions are necessary for your calculations? (Select all that apply.)

-σ is known

-normal distribution of weights

-n is largeσ is unknown

-uniform distribution of weights

(c) Interpret your results in the context of this problem.

-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

-The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

-There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

-There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

________ hummingbirds

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is

x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.26 gram.(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is large

σ is known

normal distribution of weights

uniform distribution of weights

σ is unknown

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.    

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) _______ hummingbirds

6.5---11 and 12

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 475 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.6% and standard deviation σ = 1.2%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 475 stocks in the fund) has a distribution that is approximately normal? Explain.

----- Yes , x is a mean of a sample of n = 475 stocks. By the  --central limit theory--- central limit theorem law of large numbers , the x distribution  --is not approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)_______________


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)________________


(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

Yes, probability increases as the standard deviation decreases.

Yes, probability increases as the mean increases.   

Yes, probability increases as the standard deviation increases.

No, the probability stayed the same.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.6%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) = _________________

Explain.

This is very unlikely if μ = 1.6%. One would suspect that the European stock market may be heating up.

This is very likely if μ = 1.6%. One would not suspect that the European stock market may be heating up.    

This is very likely if μ = 1.6%. One would suspect that the European stock market may be heating up.

This is very unlikely if μ = 1.6%. One would not suspect that the European stock market may be heating up.

12) The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

(a) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)_________


(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)_________


(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)______________

• Since bondholders get paid before stockholders get paid in the event of bankruptcy of a firm, the average "real" rate of return on stocks and bonds must be the same, with bonds being less risky.
• While stocks have higher average rates of return in the long run, bonds actually have higher average rates of return in the short run. As such, bonds are likely to be more profitable for the groups of people who might need to get their investment back in a relatively short period of time. 
• While stocks have a higher rate of return in the long run, they are much more volatile (riskier) in the short run. As such, they have a higher probability of having less than the original value of the investment for people who might need to withdraw the investment in the short run.
• This is actually bad advice. You should always invest in whatever has the highest average rate of return.

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000.

1. Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place. Enter your answer as a percent.
   
   %
   
2. How much does Strassel need to bid to be assured of obtaining the property?
   
   $  
   
   What is the profit associated with this bid?
   
   $  
   
3. Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $130,000, $140,000, or $150,000. What is the recommended bid, and what is the expected profit?
   
   A bid of
   • $130,000
   • $140,000
   • $150,000
   results in the largest mean profit of $  .

Please sole using excel

Consider the following relational model for a basketball league:

• Player (PlayerID, PName, Position, TeamID)
• Team (TeamID, TeamName, Venue)
• Game (GameNo, Date, Time, HomeTeamID, AwayTeamID)
• Record (GameNo, PlayerID, Points, Rebounds, Assists)

In this basketball league, each team has a unique name and each player plays for only one team. One team has at least 10 players. Two teams (home team versus away team) participate in each game at home team’s venue. Each team meets all other teams twice (i.e., double round-robin tournament), one time as home team and the other time as away team. For each game, the league records points, the number of rebounds and the number of assists for each player. If a player did not play for a game, there is no record for this player in that game.
Question 1a.Draw an ER-diagram model for the basketball league. (The relationship between two entities should be 1-to-1, 1-to-many, many-to-1 or many-to-many.)[20 marks]

1.All relationships are total participations.

2.PlayerID, TeamID and GameNo are unique attributes.

3.The relationship between Player and Team is 1-to-many relationship.

4.The relationship between Team and Game is many-to-many relationship.

Question 1b. Write a SQL to retrieve the distinct TeamID and TeamName of teams that have at least one game where the team participated as the home team getting more points than all the games where that team participated as the away team. [20 marks]

Question 2. Write a SQL to retrieve the PlayerID, PlayerName and Points of the players who achieve the highest point in a game. [20 marks]

Question 3. Write a SQL to retrieve the GameNo, TeamName, total points and total number of rebounds of a team (either home team or away team only) for each game and the team has the total number of rebounds in that game larger than 30. For a game, both teams, only home team, only away home, or none of both teams has total number of rebounds larger than 30 in that game. [20 marks]

Need SQL Tables

Final Project should be included ER, NER, Table diagrams and SQL statements.

The final project is about developing an auction Web site. The details are as follows:

BA is an online auction Web site. People can buy and sell items in this Web site. Buyers are people who like to buy items, and sellers are people who like to sell items.

•Each seller can sell items.

•Each item has a bidding start time, an end time, and an owner. Sellers are owners of their item. The start time and end time include the date as well.

•Each seller has a name, contact information, and credit card information. They also have a user name and a password.

•Contact information consists of an address, an email, and a telephone.

•An address consists of a street number and name, city, state, and zip code.

•Credit card information consists of owner name, card number, and expiration date.

•Each item has a name, condition, an initial price, a description, quantity, one or more pictures, and an owner.

•The condition could be New, Refurbished, or Explained. If the condition of an item is set to Explained, the seller should explain about the item condition in the item description.

•Each buyer has a name, contact information, and credit card information. They also have a user name and a password.

•Buyers can bid on items. Once a bid is made, buyers are accountable for their bid. In other words, buyers cannot simply remove their bid. If they change their mind, all they can do is to update their bid with the price of zero. Of course, they can do that before the auction expires.

•After an auction expires, the buyer with the highest bid is the winner.

•BA likes to have a set of statistics about the system as follows:

•The most active seller (the one who has offered the most number of items)

•The most active buyer (the one who has bought the most number of items)

•The most popular seller (the one who sold the most number of items)

•The most expensive item sold ever

•The most expensive item available

•The cheapest item sold ever

The cheapest item available

DATA SET: 105, 82, 94.5, 72.5, 92, 91, 52, 86, 100, 96, 98, 109, 96, 103, 68

Data Table:

Q1. Considering grade C or above as a passing grade, what is the probability for a student to receive a passing grade?

Q2. What is the probability of a student not receiving a passing grade?

Q3. What is the probability that the student received grade A or grade B?

Q4. What is the probability that the student received grade A, grade B, or grade C?

Q5. What is the probability that a student receive grade A & B?

Q6. What is the probability that a student receive grade A?

Q7. What is the probability that a student received grade B?

Q8. What is the probability that a student received grade C?

Q9. What is the probability that a student received grade D?

Q10. What is the probability that a student received grade F?

Q11. If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade and one F grade student?

Q12. If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade and one B grade student?

Q13. If the records whos that the probability of failing (with grade F) this course is p, [use the answer of question 11 as the probability here], what is the probability that at most 2 students out of 15 fail this course?

Q14. If the records whos that the probability of a student to get a grade B for this course is p, [use the answer to question 7 as the probability here], what is the probability that exactly 4 students out of 15 will have a grade B for the course?

Q15. What is the probability of selecting a grade A student for the first time either in 2nd or 3rd selection?

Suppose that you flip a coin 11 times. What is the probability that you achieve at least 4 tails?

A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 5 cars needs to have oil added. If this is true, what is the probability of each of the following:

A. One out of the next four cars needs oil.

Probability =

B. Two out of the next eight cars needs oil.

Probability =

C. 10 out of the next 40 cars needs oil.

Probability =

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 13% of voters are Independent. A survey asked 26 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent?

Probability =

B. What is the probability that fewer than 5 are Independent?

Probability =

C. What is the probability that more than 2 people are Independent?

Probability =