Suppose that the helium porosity (in percent) of carbon samples taken from any particular seam is normally distributed with a true standard deviation of 0.75.

a. Calculate a 95% confidence interval for the true average porosity of a seam, if the average porosity in 20 specimens of the seam was 4.85.
b. How large should a sample size be if the width of the 95% range has to be 0.40?
c. What sample size is needed to estimate true average porosity with 99% confidence for a maximum margin of error of 0.2?

The real risk-free rate of interest is 1%, inflation is expected to be 1.5% this year, 2% next year, and 3% per year for the next 5 years. The maturity risk premium is a function of time to maturity = 0.2* (1-t) %. The default risk premium on a corporate bond is 0.9%; and liquidity premium is 0.5%.

a. What is the IP over the next 4 years?

b. Find the yield on a 4-year T-bond.

c. Find the yield on a 4-year corporate bond.

Consider the following information on Stocks A, B, C and their returns (in decimals) in each state: State Prob. of State A B C Boom 20% 0.34 0.2 0.14 Good 45% 0.13 0.09 0.08 Poor 25% 0.01 0.01 0.04 Bust 10% -0.08 -0.03 -0.03 If your portfolio is invested 25% in A, 40% in B, and 35% in C, what is the standard deviation of the portfolio in percent? Answer to two decimals, carry intermediate calcs. to at least four decimals.

Gaussian Mixture Model:

the initial means and variances of two clusters in a GMM are as follows: ?(1)=−3, ?(2)=2, ?21=?22=4. Let ?1=?2=0.5.

Let ?(1)=0.2, ?(2)=−0.9, ?(3)=−1, ?(4)=1.2, ?(5)=1.8 be five points that need to cluster.

Need to find

1) p(1|1)

2) p(1|2)

3) p(1|3)

4) p(1|4)

5) p(1|5)

2) The ferrous ion-orthophenanthroline complex can be used to analyze for Fe(II) by using the absorption of this complex at 508 nm. A group of samples is known to contain between 0.1 and 0.2 g of Fe. A known sample containing 100 mg of Fe per liter was treated according to protocol, and the absorbance on a filter photometer was set to 0. The absorbance of a second standard containing 200 mg Fe per liter was then determined to be 0.795. What is the concentration of the unknown, which was then found to have an absorbance of 0.650?

Census data for a city indicate that 64.4​% of the​ under-18 population is​ white, 14.5​% black, 19.5​% Latino, 1.4% ​Asian, and 0.2​% other ethnicities. The city points out that of 25,0092 police​ officers, 64.8​% are​ white, 14.5​% ​black, 19.1​% ​Latino, and 1.4​% Asian. Do the police officers reflect the ethnic composition of the​ city's youth? Test an appropriate hypothesis and state your conclusion.​ (Assume a significance level of alphaαequals=0.05​)

A) Compute the chi-square statistic

B) Compute the P-Value

no 1
No 7.
The reverse system is used to increase the total solid orange juice from 11% to 24% consisting of 100 pipes with a length of 10 m and a diameter of 0.1 cm. the membrane permeability coefficient is known as 0.2 kg water / m² hours kPa and the product feed rate is 185 kg / min
a) determine the flow of water (kg water / hour) to reach that concentration .... (kg / min)
b) make an estimate of the difference in transmembrane hydrostatic pressure required in the operating system ... (kpa)

Use the Euler method to solve the following differential equation for the domain [2,2.5]. Use the step-size ℎ = 0.1. ?′=?ln?/? ;?(2)=?¹
b) Use the third order Taylor series method to find ?(0.1) and ?(0.2),
where ?′=1+2?? ;?(0)=0. Use the step-size ℎ=0.1.
c) Solve the problem in part (ii) using the fourth order Runge – Kutta method.
d) Solve the problem in part (ii) using the Predictor – Corrector method.

130 kg of uniform spherical particles with a diameter of 60 mm and particle density 1500 kg/m³ are fludised by water (density 1000 kg/m³, viscosity 0.001 Pa s) in a circular bed of cross-sectional area 0.2 m². The single particle terminal velocity of the particles is 0.98 mm/s and the voidage at incipient fludisation is known to be 0.47. Determine:

a. The minimum fludised velocity            

b. height when the liquid flow rate is 2x10^-5 m³/s.  

A counterflow, concentric tube heat exchanger is used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube (Di = 25 mm) is 0.2 kg/s, while the flow rate of oil through the outer annulus (Do = 45 mm) is 0.1 kg/s. The oil and water enter at temperatures of 100 and 30 C, respectively. How long must the tube be made if the outlet temperature of the oil is to be 60 C?