Furniture Depot orders a certain brand of mattress from its supplier and sells the mattresses at its retail location. The store currently orders 40 mattresses whenever the inventory level drops to 20. The cost to hold 1 mattress in inventory for one day is $0.75. The cost cost to place an order with the supplier is $80, and inventory is 30 mattresses. The daily demand probabilities are shown in the following table:

Daily Demand Probability

2 0.08

3 0.14

4 0.20

5 0.26

6 0.22

7 0.10

Lead time is decrete uniformly distributed between two and five days (both inclusive). Simulate this inventory policy for a quarter (90 days) and calculate the total quarterly cost. Also calculate the percentage of stockouts for the quarter. Replicate these calculations N times each to calculate the average values for these measures.

Executives at Microsoft are interested to get into the drone delivery business. Since it would take them too much time to set up their own operation, they decide to acquire “Flyit” corporation. “Flyit” has been operating a drone delivery service for 4 years now, and they are the most successful operators in the market. Microsoft executives offer “Flyit” two purchase options. The first option is one $40 million lump sum payment. The second option is paying five annual payments of $10 million over the next five years.

i) If the annual interest rate is 7%, find the present value of both options? [Note: you are supposed to show every step of your calculation and interpret the result]

ii)Evaluate the net present values of both option and identify which option is more cost effective for Microsoft?

As part of a course project, a statistics student surveyed random samples of 50 student athletes and 50 student non-athletes at his university, with the goal of comparing the heights of the two groups. His summary statistics are displayed in the provided table.

a). Which data analysis method is more appropriate in this situation: paired data difference in means or difference in means with two separate groups? Explain briefly.

b). Construct a 99% confidence interval for the difference in mean heights between student athletes and non-athletes at this university. Use two decimal places in your margin of error.

c). Test, at the 5% level, if student athletes at this university are significantly taller, on average, than student non-athletes. Include all of the details.

Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F).

Complete parts (a) through (e), given Σx = 247.1, Σy = 1198, Σx² = 4107.43, Σy² = 96,302.7, Σxy = 19,855.58, and r ≈ 0.796.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) What is the predicted temperature when x = 19.0 chirps per second? (Round your answer to two decimal places.)
°F

Two firms, C and D, both produce coat hangers. The price of coat hangers is $1.20 each. Firm C has total fixed costs of $750,000 and variable costs of 30¢ per coat hanger. Firm D has total fixed costs of $400,000 and variable costs of 50¢ per coat hanger. The corporate tax rate is 40%. If the economy is strong, each firm will sell 2,000,000 coat hangers. If the economy enters a recession, each firm will sell 1,400,000 coat hangers.

If the economy is strong, the total revenue of firm C will be

$1,680,000.

$2,400,000.

$2,000,000.

$1,400,000.

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain.

(e) Compute the standard deviation σ for ages of nurses shown in the distribution. (Round your answer to two decimal places.)

4. YQR has a market value of $125 million and 5 million shares outstanding. HKG has a market value of $40 million and 2 million shares outstanding. YQR thinks of taking over HKG with a premium of $10 million. The combined firm will be worth $185 million. If YQR offers 1.2 million shares of its stock in exchange for the 2 million shares of HKG, what will the stock price of YQR be after the acquisition? What exchange ratio between the two stocks would make the value of a stock offer equivalent to a cash offer of $50 million?

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain.

Compute the standard deviation σ for ages of nurses shown in the distribution. (Round your answer to two decimal places.)

Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that

NOTE: I'd like to learn how to do this in the shortest way possible on ti 84 plus calculator.

a) x>43

b) x<42

c) x>57.5

d) 42 <x<48

e) x<40 or x>55

f) 5% of the values are less than what X value?

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

h) 85% of the values will be above what X value?

Two discharge wells (1 and 2) penetrating an unconfined aquifer are pumped at constant rates of 3,000 and 500 m^3 per day , respectively. The steady-state head (i.e., water table height) measured at an observation well is 40 meters . The observation well is 50 meters from well 1 and 64 meters from well 2. The water table height measured at a second observation well is 32.9 meters , which is located 20 meters from well 1 and 23 meters from well 2. Determine the aquifer permeability K (in m/day).