Let the number of tropical cyclones per year in the Atlantic Basin (?) have a discrete uniform between 5 to 15; i.e. ? ∈ {5, 6, … , 15} with ?_X(?) = 1 /11. If each cyclone can turn into a major hurricane with probability 0.3; find the expected number of major hurricanes per year (?). Hint: Use the Law of Interated Expectation; ?[?] = ?[?[?|?]].

(b) (5 points) Calculate a 90% confidence interval for the difference between the mean diameter of the entire batch produced at plant B and the mean diameter of the entire batch produced at plant A. Write a sentence interpreting the confidence interval.

The average number of mosquitos in a stagnant pond is 80 per square meter with astandard deviation of 12. If 36 square meters are chosen at random for a mosquitocount, find the probability that the average of those counts is more than 81.6 mosquitosper square meter. Assume that the variable is normally distributed.

A)0.3%B)21.2%C)78.8%D)28.8%

Estimate the heat loss rate from a person who can be approximated as a cylinder of diameter 0.3 m and height 1.8 m. The (clothing) surface temperature is 23 °C and the cross wind flow velocity is 15 m/s. The ambient temperature is –23 °C. Neglect end effects from the cylinder. Assume steady state.

Determine the p-value for each of the following situations. (Give your answer bounds exactly.)

(a) H_a: β₁ > 0, with n = 15 and t = 1.23
_____ < p < _____

(b) H_a: β₁ ≠ 0, with n = 25, b₁ = 0.3, and s_b1 = 0.11
____ < p < _____

(c) H_a: β₁ < 0, with n = 18, b₁ = -1.55, and s_b1 = 0.73
____< p < ____

A rectangular rosette is mounted on a steel plate having a modulus f elasticity E=200GN/m2 and Poission’s ratio =0.3. The strains measured are ε1=500×10-6; ε2=400×10-6; ε3= -100×10-6. Develop a MATLAB code to compute maximum shear stress and the orientation angle for the principle axis of the stress.

Ebling Inc. finances with 0.2 fraction debt, 0.1 fraction preferred and the remaining common stock. Ebeling's before-tax cost of debt is 0.05, it cost of preferred stock is 0.12, and its cost of common stock is 0.16. If Ebeling is subject to a 0.3 fraction corporate income tax, what is the company's Weighted Average Cost of Capital?

A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.3 m³/min how fast is the water level rising when the water is 20 cm deep?

Consider a block (mass 12 kg) at rest on a flat plane. A static coefficient of friction (μs = 0.3) exists between the block and the ground. If a force of 50 N is applied to the block find:

(a) The acceleration of the block.
(b) The velocity of the block after 3 seconds.

(c) The displacement of the block from its starting location after 3 seconds.

  Consider a discrete random variable with the following probability mass function

Generate a random sample of size n =10000 from this distribution. Construct a bar diagram of the observed frequencies versus the expected frequencies.(using R)