**SHOW ALL WORK IN EXCEL QM**

Problem-4:

Every home football game for the past eight years at Eastern State University has been sold out. The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overall profitability of the football program. One particular souvenir is the football program for each game. The number of programs sold at each game is described by the following probability distribution:

Historically, Eastern has never sold fewer than 2,300 programs or more than 2,700 programs at one game. Each program costs $0.80 to produce and sells for $2.00. Any programs that are not sold are donated to a recycling center and do not produce any revenue.

1. Simulate the sales of programs at 10 football games. Use the random number table.
2. If the university decided to print 2,500 programs for each game, what would the average profits be for the 10 games simulated in part (a)?
3. If the university decided to print 2,600 programs for each game, what would the average profits be for the 10 games simulated in part (a)?

Part A:  The number of cars arriving at a self-service gasoline station during the last 50 hours of operation are as follows:

The following random numbers have been generated: 44, 30, 26, 09, 49, 13, 33, 89, 13, 37. Simulate 10 hours of arrivals at this station. What is the average number of arrivals during this period?

Part B:  The time between arrivals at a drive-through window of a fast-food restaurant follows the distribution given below. The service time distribution is also given in the table in the right column. Use the random numbers provided to simulate the activity of the first five arrivals. Assume that the window opens at 11:00 a.m. and the first arrival is after this, based on the first interarrival time generated.

Random numbers for arrivals: 14, 74, 27, 03

Random numbers for service times: 88, 32, 36, 24

What time does the fourth customer leave the system?

1. Anystate Auto Insurance Company took a random sample of 376 insurance claims paid out during a 1-year period. The average claim paid was $1560. Assume σ = $242.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

2.Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 78 students in the highest quartile of the distribution, the mean score was x = 178.10. Assume a population standard deviation of  σ = 7.93. These students were all classified as high on their need for closure. Assume that the 78 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1.8 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.)

3.Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency, duration, and type of use. One study involving heavy use of the phones showed the mean of the battery life to be 12.25 hours with a standard deviation of 2.4 hours. Then the battery needs to be recharged. Assume the battery life between charges is normally distributed.

(a) Find the probability that with heavy use, the battery life exceeds 13 hours. (Round your answer to four decimal places.)


(b) You are planning your recharging schedule so that the probability your phone will die is no more than 5%. After how many hours should you plan to recharge your phone? (Round your answer to the nearest tenth of an hour.)
hours

Suppose that a game of chance is played with a pair of fair 10-sided dice (with the sides numbered 1 to 10). In the game, you can pick any number from 1 to 10 and the two dice are then “rolled” in a cage. If $1 is bet and exactly one of the number that you picked is rolled you win $1, and if both of the dice are the number that you picked you win $20 (in each of those cases you also get your initial $1 bet back). If none of your number winds up being rolled you lose your $1 bet. Suppose that you play this game 8 times and pick the same number each time.

a) What is the probability that doubles of YOUR number (both dice come up your number) does not occur in the 8 rolls?

b) What is your total expected win or loss? Indicate in your answer both the amount (rounded to the nearest $0.01 if necessary) and whether it is a win or loss.

1.D Which of the following statements is true and why?

A. speed can be negative.

B. acceleration is always positive.

C. constant speed implies constant velocity.

D. acceleration and velocity always have the same direction.

E. constant velocity implies constant speed.

2.A If a net non-zero force is acting on an object, which of the following must be true?

A. The object is moving with constant velocity.

B. The speed is increasing.

C. The speed is changing.

D. The object has a non-zero acceleration.

E. The acceleration is changing

5.A What is impulse and what is momentum? How can the second Newton’s law be formulated these concepts?

7.A A spring-loaded toy gun is used to launch a 5-gram plastic ball. The compressed spring in the gun stores 0.025 J of energy. When the trigger is pulled the spring is released and shoots the ball back out. If all the spring energy is transferred to the ball, what is the ball's speed as it leaves the barrel?

7.B A 1.5-kg cart starts at rest at the top of the frictionless hill shown below. When it reaches the bottom it is traveling at 30 m/sec. What is the height of the hill?

7.C A 400-gram ball is released from a 180 cm height above the floor (with zero initial velocity). At the moment just before it reaches the floor its speed is measured to be 5.92 m/s. How much energy was lost into heat?

8.A A 500-kg sports car accelerates from rest to 30 m/s in 10 seconds. What is the power of the car’s engine?

8.B The brain consumes energy at 10 times the rate of the rest of the body per gram of tissue. The average power consumption of a typical adult’s brain about 20 W. How much energy on average is consumed by brain during a 2-hr exams?

8.C An elevator motor lifts a 1000-kg elevator a height of 60 meters. How much power must the motor supply to do this in 40 sec at a constant speed?

Suppose an undergraduate-admissions committee rated 400 applicants and randomly chose 12 from those in the top 15 %.

(i) Compute the probability that a person will be admitted given that he/she has the highest faculty rating among the 400 students.

(ii) Compute the probability that a person will be admitted given that he/she has the lowest faculty rating.

(b) In a production line, suppose 3 % of the products have Type A defects and 2 % of products have Type B defects. It is also known that 0.4 % of products have both types of defects. Given that a product is known to have Type A defect. Compute the probability that it has Type B defect.

(c) Dolomite is a common rock-forming mineral and the primary component of the sedimentary rock. During mining operations, dolomite is often mixed up with shale, which is another fine-grained sedimentary rock. Miners can make use of the radioactivity features of rock to help them distinguish between shale rock zone and dolomite rock zone. Based on certain guidelines and standards, if the gamma ray reading of a rock zone is less than 70 API units, the area is considered to be abundant in dolomite, and hence can be mined. On the other hand, if the gamma ray reading of a rock zone exceeds 70 API units, then the area is considered to be mostly shale and therefore will not be mined. In an exploratory research study, a random set of 750 sample data is collected from a rock quarry. It is found that 480 of the samples are dolomite and 270 of the samples are shale. Of the 480 dolomite samples, 50 of them had gamma rays readings greater than 70. As for the 270 share samples, 255 of them had gamma ray readings greater than 70. Suppose a gamma ray reading greater than 70 is obtained at a particular depth of the rock quarry.

Compute the probability that the area should be mined.

(d) The manager of a self-service carwash station found that customers take an average of 8 minutes to wash and dry their cars. Assuming that the self-service times can be modelled by exponential distribution, compute the probability that a customer will require more than 11 minutes to complete the job.

(e) In a manufacturing process where glass products are made, bubbles do occur. When this happens, the quality of the products will be affected. Suppose based on past records, on average, 1 in every 1000 of these glass products produced has one or more bubbles.

(i) Apply a suitable exact model to compute the probability that a random sample of 5000 glass products will result in fewer than 4 products with bubbles.

(ii) Apply an approximate model to compute the probability that a random sample of 5000 glass products will result in fewer than 4 products with bubbles.

(iii) Comment on the results. (1 mark)

As Nurses,

We advocate for change to provide the highest level of quality care for our patients.

We do this through the innovations we implement.

The utilization of our research, based on evidence based practice,

Nurses make change possible.

Think of an issue you wish to advocate for change. This can be an issue in the healthcare or community setting.

Then discuss HOW you will advocate for changing this issue.

Remember to include the current issue and how you will make this issue better.

What would make this issue better??

What steps are needed to advocate for change???

What is your first step to make this happen????

Identify the following securities with the highest yield and lowest yield (at issuance) and briefly explain why:

a. 10-year treasury bonds

b. 10-year corporate bonds with AAA rating

c. 10-year corporate bonds with BB rating

d. 2-month treasury notes

Rank the following bonds based on their interest rate risk, from the lowest to the highest, if all other terms of the bonds are the same: an inverse floater, a floater, and a fixed-rate bond.