Researchers investigated the issue of race and equality of access to clinical trials. The following table shows the population distribution and the numbers of participants in clinical trials involving lung cancer. Use a 0.01 significance level to test the claim that the distribution of clinical trial participants fits well with the population distribution. Is ther a race/ethnic group that appears to be very under-represented?

Suppose you take out a 20-year mortgage for a house that costs $332,294. Assume the following: The annual interest rate on the mortgage is 4%. The bank requires a minimum down payment of 18% at the time of the loan. The annual property tax is 1.6% of the cost of the house. The annual homeowner's insurance is 0.7% of the cost of the house. The monthly PMI is $70 Your other long-term debts require payments of $937 per month. If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the 28% rule and the 36% rule simultaneously? Round your answer to the nearest dollar.

For each problem, write an R code to compute each probability.

(a)   Binomial Distribution: X ~ Bin(10, 0.7)

    (i)            P(X = 2)

    (ii)           P(X < 2)

    (iii)          P(X > 2)

    (iv)          P(1 < X < 7)

(b) Normal Distribution: X ~ N(0, 4). Note that variance is 4 and, hence, the standard deviation is 2.

    (i)             P(X < 3)

    (ii)           P(X > 3)

    (iii)          P(1 < X < 3)

(c) Choose either (a) or (b) and interpret the results in a real-life scenario. Make sure to define X and interpret each probability.

1.A hospital spokesperson reported that 4 births had taken place at the RG Hospital during the last 24 hours. Find the following probabilities:

a.P(A) = that 2 boys and 2 girls are born.

b.P(B) = no boys are born.

c.P(C) = at least one boy is born.

2.The odds that a team will win in the finals is 4:3. What is their chance of winning?

3.The probability that a patient entering RG Hospital will consult a physician is 0.7, that he/she will consult a dentist is 0.5 and that he/she will consult a physician or a dentist or both is 0.9. What is the probability that a patient entering the hospital will consult both a physician and a dentist?

Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.14 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.16 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.66 probability that Sally gets it, a 0.28 probability that it comes back to Mike, and a 0.06 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.)

The investor decides to diversify by investing $3,000 in Gryphon stock and $5,000 in Royal stock, which Grypon stock has an expected return of 9.4% and a standard deviation of 5.24%, and which Royal stock has an expected return of 10% and a standard deviation of 13.5%. The correlation coefficient for the two stocks' returns is 0.7. Calculate the expected return and standard deviation of the portfolio.

And I calculated that the expected return of the portfolio is 9.78%, and STDEV of the portfolio is 9.91%.

My question is: Suppose the investor decides to invest an additional $3,000 in a treasury bill yielding 3.5%. What will be the expected return and standard deviation of this portfolio.

(ps. need details solutions.. )

Suppose that the fuel price at a specific gas station consists of :

A fixed government fuel excise of $0.416/L

Wholesale costs for supplier, which average $0.712/L, with a variance of 0.10.

Retail costs (including profit margin) at an average of $0.212/L, with a variance of 0.0012.

a) Find the average total fuel cost on any given day

b) Given that wholesale and retail costs have a correlation of 0.7, find the variance in total fuel price

c) Assuming that the total fuel price is normally distributed, what is the probability of fuel being priced at less than $1/L on any given day?

A filtration component consists of a rectangular channel having dimensions H = 10 cm, W = 50 cm, and L = 100 cm, containing carbon pellets of diameter 5 mm, is modelled using the Ergun equation. Develop the pressure drop versus mass flowrate (for ?̇ in the range of 1 – 50 kg/s) characteristic for the following porosities (due to packing arrangement): ? = 0.5, 0.7, and 0.9. The fluid properties may be taken to be ρ = 1000 kg/m3 , μ = 1.0 × 10-3 Pa⸱s. What is the pressure drop when ?̇ = 50 kg/s? Is it better to operate three filters in series or in parallel? Why?

note-please attach diagram with answer, do with easy method so I can understand question..
Q:34.6An earth canal in good condition is 17 m wide at the bottom and has side slope of 2 horizontal to
1 vertical. One side slope extends to a height of 7.8 m above the bottom level and the other side
extends to an elevation of 1.8 m, then extends flat to a distance of 150 m and rises vertically. If
the slope of the canal is 0.7 m per 1379 m, estimate the discharge in (m3/s) when the depth of water is
2.5 m. Assume Chezy's constant C = 39.

1.Answer the following questions.

a)A solid shaft transmits 75kW power at 200rpm.Determine the diameter of the shaft if the twist in the shaft is not exceeded 1⁰ in 1m length of the shaft, and shear stress is limited to 50N/mm^2.

Take rigidity modulus, G=100kN/mm^2

b)A hollow shaft with a diameter ratio of 0.7(internal outside) is required to transmit 500kW at 300 rpm with a uniform twisting moment. Allowable shear stress in the material is 70N/mm^2 and twist in a length of 2.5m is not to exceed 1⁰.Determine the maximum external diameter of the shaft satisfying these conditions. Take modulus of rigidity G= 80KN/mm^2