Question
(a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257.
Calculate the unbiased estimator of the population variance.

(b) Suppose the GPA of all students enrolled in a particular course can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Compute the probability that the
mean GPA of a random sample of 40 students selected from this course will be:

(i) lower than 3.2
(ii) between 3.3 and 3.6

(c) Suppose you throw a die 600 times. Apply a suitable technique to compute the
approximate probability of obtaining between 90 and 110 fours.

A 4m thick clayey layer was initially water saturated with water content w = 34%, and in situ effective stress σzo’ = 31 kPa. Clearly state your assumptions to determine: a) The total settlement in this clay layer, if the final void ratio after consolidation is ef = 0.75. b) If OCR = 2.2, the construction of an embankment at this site induces 48.5 kPa additional load, what will be the total settlement at this site? Assuming Cc = 0.3 and Cr = 0.06. (c) What will be the settlement after 10 years of consolidation, assuming Cv = 3.2 × 10-7 cm2 /sec and double drainage condition.

(a) Find the margin of error for the given values of​ c, σ​, and n. c = 0.90​, σ = 3.8​, n = 100

E= _ (Round to three decimal places as​ needed.)

(b) Construct the confidence interval for the population mean μ.

c = 0.90 ​, x=9.1​, σ = 0.3 ​, and n = 47

A 90​% confidence interval for μ is _, _ (Round to two decimal places as​ needed.)

(c)  Construct the confidence interval for the population mean μ.

c=0.95 , x=16.2, σ =2.0, and n =35

A 95​% confidence interval for μ is _, _ (Round to two decimal places as​ needed.)

A.EACH $ 5  BILLION INCREASE IN MONEY SUPPLY REDUCES THE RATE OF INTEREST BY 0.3 PERCENTAGE POINT

B.EACH 1 PERCENTAGE DECLINE IN INTEREST RATES STIMULATE 24 BILLION WORTH OF NEW INVESTMMENT.

C.MPC = 0.75 .

D.THE AGGREGATE SUPPLY CURVE IS SO FLAT PRICES DO NOT RISE NOTICABLY (NO INFLATION) WHEN DEMAND INCREASES. MAKE SURE DO ALL CALCULATION AS WELL PROPPER GRAPHS

Occupancy data from a single loop detector was obtained from a one way street. The loop detector has a length of 6 feet and was observed to have six vehicles cross over it in a period of 30 seconds. The duration and the length of each vehicle are shown in the table below. Use the average vehicle length in your calculations. Estimate the values of q, k and u (flow, density and speed)

1. A cylindrical shell is 3 m long; 1 m in diameter and the thickness of metal is 10 mm. It is subjected to an internal pressure of 150 N/cm². Calculate the change in dimensions of the shell and the maximum intensity of shear stress induced. Given E= 200 GPa and Poisson’s ratio =0.3.

b. Two shafts of the same material and same lengths are subjected to the same torque. If the first shaft is of a solid circular section, the second shaft is of hollow circular section, whose internal diameter is 2/3 of the outside diameter and the maximum shear stress developed in each shaft is the same, compare the weights of the shafts

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.

a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.

1. Today is your 25^th birthday. Your goal is to retire when you turn 70 years old and have sufficient monthly income until your expected demise on your 99^th birthday. In order to realize your goal, you are planning to make deposits into a target-date retirement fund that is expected to generate 7.8% annual return, compounded monthly. You want to be able to make monthly withdrawals from this fund starting one month after your retirement until your expected demise. These monthly withdrawals will increase by 0.3% a month in order to compensate for the expected increase in price levels. Retirees are able to survive on $2,000 monthly income today. Your first withdrawal one month after your 70^th birthday, therefore, will be $2,000 adjusted for 0.3% expected monthly inflation.

1. You are planning to make equal annual deposits starting one year from today until you retire. Calculate your deposits.
2. You are planning to make annual deposits starting one year from today until you retire. However, you believe that you can increase your deposits 4% a year in line with the expected increase in your income. Calculate your first deposit.
3. You are expecting inheritance money in the amount of $200,000 when you turn 50 years old and planning to deposit this amount immediately into the fund. Based on this expectation, recalculate your answer to part b.

A semiprofessional baseball team near your town plays two home games each month at the local baseball park. The team splits the concessions 50/50 with the city but keeps all the revenue from ticket sales. The city charges the team $100  each month for the three-month season. The team pays the players and manager a total of $1000 each month. The team charges $10 for each ticket, and the average customer spends $6 at the concession stand. Attendance averages 30 people at each home game.

The team earns an average of (1)$___ in total revenue (tickets plus share of concessions) for each game and (2) $___ of revenue each season.

With total costs of (3)$____ each season, the team finishes the season with (4)$____ of profit.

Indicate whether the following losses are covered under Section II of the homeowners policy. Assume there are no special endorsements and no deductible. Give reasons for your answers.

1. The named insured’s dog bites a neighbor’s child

2. The named insured's dog eats a neighbor's coat.

3. A neighbor’s child falls off a swing in the named insured’s yard and breaks an arm.

4. The named insured falls on his icy sidewalk and breaks a leg.

5. While driving to the supermarket, the named insured injures another motorist with the automobile.

6. The named insured paints houses for a living. A can of paint accidentally spills onto a customer’s roof and discolors it.

7. The named insured falls asleep while smoking a cigarette in a rented hotel room, and the room is badly damaged by the fire.