1) In a recent poll, the Gallup organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Answer the questions below, showing work. Bare answers are not acceptable. (Showing work means writing the calculator command you used with correct input values in the correct order.)

a) Explain why this is a binomial experiment.

b) Find and interpret the probability that exactly 15 of those surveyed felt the overall state of moral values in the United States is poor.

c) Find and interpret the probability that no more than 10 of those surveyed felt the overall state of moral values in the United States is poor.

d) Find and interpret the probability that more than 16 of those surveyed felt the overall state of moral values in the United States is poor.

e) Find and interpret the probability that 13 or 14 of those surveyed felt the overall state of moral values in the United States is poor.

f) Would it be unusual to find 20 or more adult Americans who believe the overall state of moral values in the United States is poor? Why or why not?

g) Now based on a random sample of 500 adult Americans, compute the mean and standard deviation of the random variable X, the number of adults who believe the overall state of moral values in the United States is poor. Interpret the mean.

h) Would it be unusual to identify 240 adult Americans who believe the overall state of moral values in the United States is poor, based on a random sample of 500 adult Americans? Why? Now using the Normal Approximation to the Binomial, approximate the probability that:

i) Exactly 250 of those surveyed feel the overall state of moral values in the United States is poor.

j) Between 220 and 250, inclusive, of those surveyed feel the overall state of moral values in the United States is poor.

k) At least 260 adult Americans who believe the overall state of moral values in the United States is poor, based on a random sample of 500 adult Americans. Would this be unusual? Why?

2 ) According to www.meretrix.com traffic fatalities occur at a rate of 1.32 fatal accidents per 100 million miles. Find the probability that, during the next 100 million miles, there will be

a) exactly zero accidents. Interpret the results.

b) at least one fatal accident. Interpret the results.

C) more than one fatal accident. Interpret the results.

A left turn lane is to be designed at a signalized intersection to accommodate leftturning
vehicles during the peak period of traffic. If the design peak hour volume for the left
turn movement is 150 vehicles per hour and the red time interval per signal cycle for the left turn
movement is 60 seconds.

a) Compute the average number of left turn vehicle arrivals per red interval of each signal
cycle during the design peak hour.

b) Assume that left turn vehicles arrive the intersection in a random fashion (i.e., following
Poisson distribution). Compute and plot the probability mass function (PMF) for the
number of left turn vehicles arriving during the red interval (use of Excel spreadsheets is
preferred).

c) If the design of the left-turn lane requires accommodating (or storing) the left-turn queue
95% of time during the peak hour, recommend the minimum left-turn lane length in feet
(assuming 25 feet per vehicle, including space between vehicles).

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 15 calls per hour. The arrival rate is 30 calls per hour.

How many extension lines should be used if the company wants to handle 90% of the calls immediately?

What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.

What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.

Your company doesn't face any taxes and has $511 million in assets, currently financed entirely with equity. Equity is worth $41.10 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below:

The firm is considering switching to a 25-percent debt capital structure, and has determined that they would have to pay a 8 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? (Round your intermediate calculations and final answer to 2 decimal places except calculation of number of shares which should be rounded to nearest whole number.)

"An aircraft control actuator is part of the flight control system that enables an airplane to fly. It is important that the actuators are reliable. Reliability can be defined as the probability a system is functioning, so it is a number between 0 and 1. One way to increase reliability of the actuator is to increase the torque. The reliability R as a function of the maximum torque T (in Newton-meters) is given by
R(T)=0.91*exp(0.027T)
where torque T is between 0.1 and 3.5. The development and installation cost as a function of reliability equals [$1760+ $11007*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 6 and in year 12. In each year the maintenance cost as a function of reliability R is [$1350/ln(1.45R)]. Assume the interest rate is 10%.
What is the optimal torque design (a number between 0.1 and 3.5 rounded to the nearest tenth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)"

"An aircraft control actuator is part of the flight control system that enables an airplane to fly. It is important that the actuators are reliable. Reliability can be defined as the probability a system is functioning, so it is a number between 0 and 1. One way to increase reliability of the actuator is to increase the torque. The reliability R as a function of the maximum torque T (in Newton-meters) is given by
R(T)=0.91*exp(0.027T)
where torque T is between 0.1 and 3.5. The development and installation cost as a function of reliability equals [$1760+ $11007*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 6 and in year 12. In each year the maintenance cost as a function of reliability R is [$1350/ln(1.45R)]. Assume the interest rate is 10%.
What is the optimal torque design (a number between 0.1 and 3.5 rounded to the nearest tenth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)"

An aircraft control actuator is part of the flight control system that enables an airplane to fly. It is important that the actuators are reliable. Reliability can be defined as the probability a system is functioning, so it is a number between 0 and 1. One way to increase reliability of the actuator is to increase the torque. The reliability R as a function of the maximum torque T (in Newton-meters) is given by R(T)=0.91*exp(0.027T) where torque T is between 0.1 and 3.5. The development and installation cost as a function of reliability equals [$1980+ $14030*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 3 and in year 7. In each year the maintenance cost as a function of reliability R is [$1160/ln(1.45R)]. Assume the interest rate is 12%. What is the optimal torque design (a number between 0.1 and 3.5 rounded to the nearest tenth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)

Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 40 calls per week on professors. Several representatives say that the estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42 and variance is 4.41. Conduct an appropriate hypothesis test, at the 5% level of significance to determine if the mean number of calls per salesperson per week is more than 40.

(a) Provide the hypothesis statement

(b) Calculate the test statistic value

(c) Determine the probability value

(d) Provide an interpretation of the P-value (1 Mark)

Note: if you need to use symbols , please use "u" for population mean "μ", Ho and Ha for for the null and alternate hypothesis, "Y-hat" for "ŷ", "alpha" for α Please provide your answers to the above questions by typing your answers using simple text. You need not show the work in detail.

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.

1. What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.
2. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.
3. How many extension lines should be used if the company wants to handle 85% of the calls immediately?

Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.

1. What number of calls, in decimal form, receive a busy signal for the current telephone system with two extension lines? If required, round your answer to four decimal places.
2. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used? If required, round your answer to four decimal places.
3. How many extension lines should be used if the company wants to handle 85% of the calls immediately?