Student scores on Professor Combs' Stats final exam are normally distributed with a mean of 77 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 82. b.) The probability that 20 students chosen at random have a mean score above an 82. c.) The probability that one student chosen at random scores between a 72 and an 82. d.) The probability that 20 students chosen at random have a mean score between a 72 and an 82.

q2. World class marathon runners are known to run that distance (26.2 miles) in an average of 143 minutes with a standard deviation of 13 minutes.

If we sampled a group of world class runners from a particular race, find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one runner chosen at random finishes the race in less than 137 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 137 minutes.

c.) The probability that 50 runners chosen at random have an average finish time of less than 137 minutes.

An irrigation canal contractor wants to determine whether he should purchase a used Caterpillar mini excavator or a Toro powered rotary tiller for servicing irrigation ditches in an agricultural area of California. The initial cost of the excavator is $26,500 with a $9000 salvage value after 10 years. Fixed costs for insurance, license, etc. are expected to be $18,000 per year. The excavator will require one operator at $15 per hour and maintenance at $1 per hour. In 1 hour, 0.15 mile of ditch can be prepared. Alternatively, the contractor can purchase a tiller and hire 2 workers at $11 per hour each. The tiller costs $1200 and has a useful life of 5 years with no salvage value. Its operating cost is expected to be $1.20 per hour, and with the tiller, the two workers can prepare 0.04 mile of ditch in 1 hour. The contractor’s MARR is 10% per year. Determine the number of miles of ditch per year the contractor would have to service for the two options to break even. Solve the problem using Annual worth (AW), present worth (PW), anf future worth (FW).

A mechanical. person is intrested in testing if tuning a car engine would improve the gas miliage. A simple random sample of 8 cars were selected to determine the milage (miles per gallon). Then each of the 8 cars were given a tune up
(SHOW WORK, please helpp)
Data:
After Tune up: 28.21, 29.4, 30.42, 29.67, 31.31, 29.68, 28.82, 29.38
Mean: 29.61
Standard Deviation: 0.94

Before Tune Up: 26.9, 26.37, 29.13, 28.46, 28.17, 27.67, 27.84, 27.18,
Mean: 27.72
Standard deviation: 0.89

Difference (After-Before): 1.31, 3.03, 1.29, 1.21, 3.14, 2.01, 0.98, 2.2,
Mean: 1.9
Standard Deviation: 0.84

1.) Are the 2 samples (Before and after Tune Mileage) independent or dependent? Explain

2.) Show which plot you would use to check your assumptions? Show picture of it

3.)Are their and serious violations of any other assumption plots? Explain

4.) What is your output? state below Explain why you chose this output

5.) What is your conclusion at a 5% confidence level?

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the​ freeway, resulting in a freer flow of​ cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel​ times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the​ on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds​ (in miles per​ hour).

Determine the​ P-value for this test.

​P-valueequals=

​(Round to three decimal places as​ needed.)

Course Project Case Study: Mr. Lopez is an 85 year-old Hispanic man who was admitted to the hospital with complaints of fatigue, decreased appetite, and a 25 pound weight loss over the past six months. He also reports change in his short term memory. He used to be active with his local retired friends and walked 1.5 miles a day but now spends most of his time in his recliner watching television. He has a medical history of coronary artery disease and hypertension.

rders include:

Regular diet, calorie count

Ensure shakes TID daily

Ambulate TID daily, stand by assist

Daily weights

Warfarin 2 mg PO daily

Digoxin 125 mcg PO daily

Atorvastatin 20 mg PO daily

Escitalopram 10 mg PO daily

Metoprolol 50 mg PO BID

Do not resuscitate

Choose five labs or diagnostic tests that might be ordered for your case study client and explain why. Note normal results, expected abnormal values, and what that would signify for your client.

Tom Hagstrom needs a new car for his business. One alternative is to purchase the car outright for $28,000 and to finance the car with a bank loan for the net purchase price. The bank loan calls for 36 equal monthly payments of $881.30 at an interest rate of 8.3% compounded monthly. Payments must be made at the end of each month. The terms of each alternative are Buy Lease $28,000 $696 per month 36-month open-end lease. Annual mileage allowed = 15,000 miles If Tom takes the lease option, he is required to pay $500 for a security deposit, which is refundable at the end of the lease, and $696 a month at the beginning of each month for 36 months. If the car is purchased, it will be depreciated according to a five-year MACRS property classification. The car has a salvage value of $15,400, which is the expected market value after three years, at which time Tom plans to replace the car, irrespective of whether he leases or buys. Tom’s marginal tax rate is 28%. His MARR is known to be 13% per year. (a) Determine the annual cash flows for each option. (b) Which option is better?   

1.)
A mechanical. person is intrested in testing if tuning a car engine would improve the gas miliage. A simple random sample of 8 cars were selected to determine the milage (miles per gallon). Then each of the 8 cars were given a tune up

Data
After Tune up: 28.21, 29.4, 30.42, 29.67, 31.31, 29.68, 28.82, 29.38
Mean: 29.61
Standard Deviation: 0.94

Before Tune Up: 26.9, 26.37, 29.13, 28.46, 28.17, 27.67, 27.84, 27.18,
Mean: 27.72
Standard deviation: 0.89

Difference (After-Before): 1.31, 3.03, 1.29, 1.21, 3.14, 2.01, 0.98, 2.2,
Mean: 1.9
Standard Deviation: 0.84

1.) Are the 2 samples (Before and after Tune Mileage) independent or dependent? Explain

2.) Show which plot you would use to check your assumptions? Show picture of it

3.)Are their and serious violations of any other assumption plots? Explain

4.) What is your output? state below Explain why you chose this output

5.) What is your conclusion at a 5% confidence level?

In a two-page paper, identify the physics principles contained within the following scenario. Explain how these principals connect to Einstein's theory of relativity or in modern applications in physics. If you use a GPS option on your car or a mobile device, you are using Einstein's theory of relativity. Finally, provide another example from your own experience, then compare and contrast your scenario to the provided example below.

Scenario:

Mandy took a trip to Rome, Italy. She gazed out over the open ocean 20,000 feet below as her airplane began its descent to her final destination of Rome. It had been a long flight from New York to Rome, but she as she stretched, and her bones creaked as though she was old, she knew that in fact, she was a tiny bit younger than her compatriots back home, thanks to traveling at hundreds of miles per hour. In fact, time for her was running slowly compared to her friends in New York for two reasons: the speed at which she had traveled and the height of the airplane above the Earth. Neither, though, were noticeable.

To illustrate the effects of driving under the influence​ (DUI) of​ alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine​ teenagers, the time​ (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts​ (a) and​ (b).

​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

​(a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the​ experiment?

​(b) Use a​ 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as​ "impaired minus​ normal.

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

TaxesˆTaxes^  = ______ + ______ Size.

b. Interpret the slope coefficient.

• As Property Taxes increase by 1 dollar, the size of the house increases by 6.86 ft.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.86.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  TaxesˆTaxes^ ________