The Chahad Bank wants to open a new branch in a distant city with very different economic conditions. Currently, the bank has an expected return of 15% with a standard deviation of 7%. The new branch is expected to have a return of 20% with a standard deviation of 10%. The correlation between the bank's returns and the returns from the new branch is -0.3. The new branch is expected to contribute 10% of the bank's revenues. What is the expected return for the bank if they add the new branch?

please show work

a. You are studying an economy with an income tax rate, ti, of 32% and an MPS of 0.3. It is currently suffering from a “recessionary gap” of $500 m. (i.e., Eqm Y Y full employment, FE, aka Yn). Make the necessary calculations for the to policy that it should institute; who does what? Provide the full name of this policy.

b. Compare this economy to one without income taxes to explain the term “automatic stabilizer.” [Hint: Let I change and compare the I multipliers in each of these economies.]

The bearing capacity, ?, of soil under a square foundation of size 9 ft^2 is determined to be a random variable with a mean of 3 ksf and a standard deviation of 0.3 ksf. The applied axial load, ?, acting on the foundation is also a random variable with a mean of 16 kip and a standard deviation of 2 kip. Assume ? and ? are statistically independent normal variables. Using the limit state function of the form ?() = 9?– ?, use the normal format approach to calculate the reliability index and the corresponding probability of failure of the foundation.

In a sample of 75 steel wires, the average breaking strength is 50 kN, with a standard deviation of 1.9 kN. a) Find a 99% confidence interval for the mean breaking strength of this type of wire. b) An engineer claims that the mean breaking strength is between 49.7 kN and 50.3 kN With what level of confidence can this statement be made? c) How many wires must be sampled so that a 99% confidence interval specifies the mean breaking strength to within 0.3 kN?

Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.) (a) P(0.0 ≤ Z ≤ 1.8) (b) P(−0.1 ≤ Z ≤ 0.0) (c) P(0.0 ≤ Z ≤ 1.46) (d) P(0.3 ≤ Z ≤ 1.58) (e) P(−2.02 ≤ Z ≤ −1.72) (f) P(−0.02 ≤ Z ≤ 3.51) (g) P(Z ≥ 2.10) (h) P(Z ≤ 1.63) (i) P(Z ≥ 6) (j) P(Z ≥ −9)

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of cheese. The estimate must be within 0.3 milligram of the population mean. Assume the population standard deviation is 2.9 milligrams. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Determine the minimum sample size required to construct a 98% confidence interval for the population mean. Which level of confidence requires a larger sample size? 90% 98%

A worker has asked her supervisor for a confidential letter of recommendation for a new job. She estimates that there is an 80% chance that she will get the job if she receives a strong recommendation, a 40% chance if she receives a moderately good recommendation, and a 10% if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate and weak are 0.6, 0.3 and 0.1 respectively. Given that she fails to get the job, what is the probability that she received a weak recommendation?

A curve of radius 30 m is banked so that a 950 kg car travelling at
40 km/h can go round it even if the road is so icy that the coefficient of static friction is approximately zero. You are commissioned to tell the local police the range of speeds at which a car can travel around this curve without skidding. Neglect the effects of air drag and rolling friction. If the coefficient of static friction is 0.3, what is the range of speeds you tell them?

1. Approximately 25% of the adult population is allergic to pets with fur or feathers, but only 4% of the adult population has a food allergy. A quarter of those with food allergies also have pet allergies.What is the probability a person has food allergies but is not allergic to pets?

A. 0.01

B. 0.03

C. 0.04

D. 0.0625

E. 0.24

2. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were children in a car involved in an auto accident if the driver was not 55 years or older?

A. 0.66

B. 0.34

C. 0.333

D. 0.27

E. 0.01

3. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were no children in a car involved in an auto accident if the driver was not 55 years or older?

A. 0.933

B. 0.66

C. 0.525

D. 0.34

E. 0.25

1- Most real estate offers are conditional on the buyer obtaining the necessary financing to complete the purchase. Based on past​ experience, one of​Canada's largest real estate agencies believes that​ 4% of the sales fail because the buyer is unable to obtain the financing approval from their mortgage broker or lender. The real estate agency has recently submitted 60 different​ offers, all of which are conditional on financing.

What is the sampling distribution model of the proportion of clients in this group who may not receive the necessary funding to purchase the​ house? Round to one decimal.

A. Mean​ = 4.0%; standard deviation​ = 0.3%

B. Mean​ = 4.0%; standard deviation​ = 2.5%

C. Mean​ = 96.0%; standard deviation​ = 2.5%

D. Mean​ = 96.0%; standard deviation​ = 0.3%

2- The director of admission of a large university is interested in determining the proportion of students who would like to live on campus in the coming academic year. Rather than examine the records for all​ students, the director randomly selects 150 students and finds that 108 of them would like to live on campus. Using a​ 90% confidence​ interval, what is the estimated true proportion of students who would like to live on campus in the coming academic​ year?

A.0.72​ ± 0.04457

B.0.72​ ± 0.060301

C.0.72​ ± 0.089582

D.0.72​ ± 0.028135