1. The mean life span of a brand name tire is 50,000 miles. Assume that the life spans of the tires are normally distributed, and the population standard deviation is 800 miles.
   • a. If you select one tire, what is the probability that its life span is less than 48,500 miles?
   • b. If you select 100 tires, what is the probability that their mean life span is more than 50,200miles?
   • c. What is the distribution of the sample mean in part b?
2. The proportion of students at a college who have a GPA higher than 3.5 is 19%.
   • a. You take repeated random samples of size 25 from that college and find the proportion of student who have a GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions?
   • b. You take repeated random samples of size 50 from that college and find the proportion of student who have a GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions?
   • c. Compare the results of parts a and b, and sketch the sampling distributions.

1. The manufacturer of a gasoline additive claims that the use of this additive increases gasoline mileage. A random sample of six cars was selected, and these cars were driven for 1 week without the gasoline additive and then for 1 week with the gasoline additive. The following table gives the miles per gallon for these cars without and with the gasoline additive.

a. Assume that the population of paired differences is approximately normally distributed. You would like to test whether the use of gasoline additive increases the gasoline mileage. Let μ_d denote the mean difference in miles per gallon for cars with and without the gasoline additive. Calculate the test statistic. Round your intermediate calculations and final answer to the nearest hundredth.

b. Let μ_d denote the mean difference in miles per gallon for cars with and without the gasoline additive. The test statistic for this case is 2.97. Calculate the p-value. Round your final answer to the nearest ten thousandth (e.g, 0.1234).

I am a travel agent, I book in-city ride tickets and also ship your luggage to the next destination. 1-NYC All Around Town it is $29.00 2-Big Bus NYC Tour it is $49.00 3-NYC one day guided Sightseeing Tour it is $89.00 4-Circle Line Complete Manhattan Island Cruise is $44.00 5-Viator VIP: Empire State Building, Statue of Liberty and 9/11 Memorial is $129.00 I also provide a quote for your shipment to be mailed to your next destination. In order to calculate our quote, we need to know the total weight of the shipment in pounds, the distance in miles and whether or not there are hazardous materials in the shipment (e.g. batteries). The calculation for the quote is as follows: Quote = .65 * # of miles + .83 * # of pounds If there is hazardous materials in the shipment, there is an extra cost of .20 * # of pounds If the distance for the delivery is less than 150 miles and the total weight for the shipment is greater than 500 pounds, then there should be a 10% discount off of the total quote. Create a c# console app using conditional statement

Kansas Enterprises purchased equipment for $60,000 on January 1, 2015. The equipment is expected to have a five-year life, with a residual value of $5,000 at the end of five years.

(1) Using the straight-line method, depreciation expense for 2015 would be: $   




(2) Using the double-declining balance method, depreciation expense for 2016 would be: $   



7 / 10

4. Crestview Estates purchased a tractor on January 1, 2015, for $65,000. The tractor’s useful life is estimated to be 30,000 miles and has a residual value of $5,000. If Crestview used the tractor 5,000 miles in 2015 and 3,000 miles in 2016, what is the balance for accumulated depreciation at the end of 2016 using the activity-based method?

$   



5. The Surf’s Up issues 2,000 shares of 5%, $100 par value preferred stock at the beginning of 2014. All remaining shares are common stock. The company was not able to pay dividends in 2014, but plans to pay dividends of $28,000 in 2015. Assuming the preferred stock is cumulative.  

(1) The annual cash dividend normally paid to preferred stock is:

$   



(2) The cash dividend paid to common stockholders in 2015 is:

$   

1. x is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for: n = 1, x = 0, p = 0.35 (b) Calculate the probability of x for: n = 7, x = 6, p = 0.7

(c) Calculate the probability of x for: n = 4, x = 1, p = 0.35

(d) Calculate the probability of x for: n = 3, x = 3, p = 0.7

(e) Calculate the probability of x for: n = 3, x = 0, p = 0.2

(f) Calculate the probability of x for: n = 6, x = 0, p = 0.7

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

Plot using RStudio

Consider a binomial random variable, X.

i. Plot the pmf of X ∼Bin(n = 10, p = 0.3).

ii. Plot the pmf of X ∼Bin(n = 10, p = 0.7).

iii. Plot the pmf of X ∼Bin(n = 100, p = 0.3).

iv. What happens to the shape of the pmf of X ∼Bin(n, p) when p gets larger?

v. What happens when n gets larger

Use Minitab to do a complete analysis of the following problem. Heat treating is often used to carburize metal parts such as gears. The of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of the part. Because of the critical nature of this feature, two different lab tests are performed on each furnace load. One test is run on a sample pin that accompanies each load. The other test is a destructive test that cross-sections an actual part. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). Data is in excel file HW 6-Q6 Heat Treating.xlsx, shows the results of the pitch carbon analysis test for 32 parts. The regressors are furnace temperature (TEMP), carbon concentration and duration of the carburizing cycle (SOAK-PCT, SOAKTIME), and carbon concentration and duration of the diffuse cycle (DIFFPCT, DIFFTIME)

1.State the problem—what are you trying to find out?

2.Fit a regression model using all of the five regressors. Summarize this analysis by providing the equation, ??², and list the standard errors. What do you notice about the p values for the regressors? What does the analysis of variance indicate?

3.Use the model to predict PITCH when TEMP=1650, SOAKTIME=1, SOAKPCT=1.1, DIFFTIME=1 and DIFFPCT=.8.

4.Do you have any problems with multicollinearity?

5.Construct a t-test on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.05.

6.Find a 95% confidence interval on each of the coefficients that were identified to be significant. Also construct a confidence interval and prediction interval on the future observation for the data given in Q3.

7.Prepare a normal probability plot of the residuals and check the adequacy of the model.

8.Utilize stepwise regression to identify a model. How does this model differ from the first one you created? Construct a normal probability plot on the residuals to check model adequacy. Write out the equation.

9.What are the possible benefits of using a model that has fewer regressors?

If x is a binomial random variable, compute ?(?) for each of the following cases:

(a)  ?(?≤1),?=3,?=0.4

?(?)=

(b)  ?(?>1),?=4,?=0.2

?(?)=

(c)  ?(?<2),?=4,?=0.8

?(?)=

(d)  ?(?≥5),?=8,?=0.6

?(?)=

a volume of 400 ml ringers lactate was started at 2000 it is infusing at a rate of 90 miles per hour what is the total infusion time what is the completion time