Sec 2.1 Pitman "Probability"

A man fires 8 shots at a target. Assume that the shots are independent, and each shot hits the bull’s eye with a probability of 0.7

Given that he hits the bull’s eye at least twice, what is the chance that he hits the bull’s eye exactly 4 times?

P(hits the bull’s eye exactly 4 times | hits the bull’s eye at least twice)

The answer has P(hits the bull’s eye exactly 4 times) / P(hits the bull’s eye at least twice)

How is this determined???

A mixer operating at steady state has two inlets and one outlet.

- At inlet 1, superheated water vapor at 2 bar and 200°C flows with an average velocity of 1m/s

- At inlet 2, saturated water with a quality of x = 0.5 at 2 bar flows with an average velocity of 1m/s

- At the outlet, saturated water with a quality of x = 0.7 flows through a pipe 5 cm in diameter.

a) Calculate the mass flow rate through the outlet pipe.

b) Calculate the rate of heat loss to the surrounding from the mixer.

A single axis personal transport device starts from rest with the rider leaning slightly forward. Together, the two wheels weigh 25 lbs, and each has a radius of 10 in. The mass moment of inertia of the wheels

about the axle is 0.15 slug ft². The combined weight of the rest of the device and the rider (excluding the wheels) is 200 lbs, and the center of gravity G of this weight is located at x = 4 in. in front of the

axle A and y = 36 in. above the ground. An initial clockwise torque M is applied by the motor to the wheels. The coefficients of static and kinetic friction are 0.7 and 0.6, respectively.

Louise (80 lbs) and Tina (100 lbs) are going to have a jumping contest. To determine who has to do the dinner dishes. Answer the following questions about their contest.

1.During the propulsive phase of the jump if Louise exerts an average of 1.3 times her body weight for .4 seconds and Tina exerts an average of 1.1 times her body weight for 0.7 seconds what will their take-off velocities be?

2. Who jumps higher? Who is in the air longer? (Be sure to calculate each of their jump heights and each of their time in the air to determine

1. An investor purchases 400 shares at $21.40 a share, holds the stock for 30 weeks, and then sells the stock for $24.60 a share. Use the commission schedule below from Company A to find the annual rate of interest earned by the investment.

Company A

Principal

Under $3,000

$3,000-$10,000

Over $10,000

Commission

$25 + 1.8% of principal

$37 + 1.4% of principal

$107 + 0.7% of principal

2. Find the annual percentage yield (APY) for money invested at an annual rate of (a) 3.05% compounded quarterly. (b) 2.95% compounded continuously. As an investor what is the preferable interest plan?

1. In 2004, Murthy, Krumholz, & Gross investigated disparities in access to clinical trials in an article entitled “Participation in cancer clinical trials: race-, sex-, and age-based disparities”.

Does the distribution of participants in clinical trials correspond to the population distribution, given that…

a.

b.

3. What would you conclude based on these findings?

1. An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A)=0.4 and P(B)=0.7.

a. If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning.

b. What is the probability that at least one of the two projects will be successful?  

c. Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?

A mixer operating at steady state has two inlets and one outlet.

- At inlet 1, superheated water vapor at 2 bar and 200°C flows with an average velocity of 1m/s

- At inlet 2, saturated water with a quality of x = 0.5 at 2 bar flows with an average velocity of 1m/s

- At the outlet, saturated water with a quality of x = 0.7 flows through a pipe 5 cm in diameter.

a) Calculate the mass flow rate through the outlet pipe.

b) Calculate the rate of heat loss to the surrounding from the mixer.

> Gymnosperm seeds are found in fruits, which are mature ovaries. (True/False)

>Small or trailing plants generally have a taproot system that spreads out like a thick mat below the soil surface. (True/False)

> If a flaccid cell (Ψ = −0.7 MPa) is placed in a solution with a lower solute concentration (Ψ = −0.1 MPa), the cell will gain water and become turgid. (True/False)

> The sporophytes of mosses can live independently of the gametophytes. (True/False)

> Changes in turgor pressure of guard cells regulate stomatal opening and closing in leaves of angiosperms. (True/False)

Answer the following question based on the following information: An investor is considering the following three stocks to invest. Suppose that the current T-bill rate is 5% and the market rate of return is 13%.

Stock A Stock B Stock C Beta

1.3 1.0    0.7

Suppose that the investor has invested $100,000 in stock A and $100,000 in stock B. How much should he/she invest in stock C so that he/she can expect 14% rate of return from the portfolio?

Group of answer choices

$5,124.76

$9.090.91

$0.00

$12,564.94

$11,764.71