A study involving 5 patients showed that 40% of the population has type O+ blood. Assume that the study maybe modeled by a probability experiment. Let x random variable that represents the possible number of patients that have type O+.

A. In words describe the success and failure for this experiment.

Success=

Failure=

B. What is the probability that exactly 2 patients will have type O+ blood?

C. What is the probability that none of the patients will have type O+ blood?

D. what is the probability that fewer than 3 patients will have type O+ blood?

E. Find the mean, variance, and standard deviation.

Each day in April, you have an independent 1/4 chance of deciding to take a 6am run.

1. (a) What is the probability you go on exactly 12 runs in the month of April (which has

   30 days)?

2. (b) What is the expected number of days you go running during April?

3. (c) What is the probability that you go running at least once during April 1–7?

4. (d) What is the probability that that your first run of the month occurs on April 5?

5. (e) What is the probability that your first run of the month occurs on or before April 20?

1.A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.08. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 18-year period. Hint: Use the binomial distribution with n = 18 and p = 0.08.

2. According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select six peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Compute the probability that exactly three of the six M&M’s are green.

Compute the probability that three or four of the six M&M’s are green.

Compute the probability that at most three of the six M&M’s are green.

Compute the probability that at least three of the six M&M’s are green.

3. A small regional carrier accepted 14 reservations for a particular flight with 11 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 43% chance, independently of each other.

Find the probability that overbooking occurs.

Find the probability that the flight has empty seats.

A piston-cylinder apparatus contains argon at initial conditions of 15 psia, 70F, and 0.30 ft³. The argon is then compressed slowly and frictionlessly to a final pressure of 150 psia. Heat transfer between the argon and the surroundings at 60F causes the temperature to remain constant throughout the compression process. Determine (a) the argon mass (lbm), (b) the final volume (ft³), (c) the work for the process (ft-lbf), (d) the heat transfer (BTU), and (f) the total entropy generation for the process (BTU/R). (f) Why is this process irreversible?

Q2. Two kilograms of air within a piston-cylinder configuration execute a Carnot power cycle between temperatures 750 K and 300 K. The isothermal expansion is associated with a heat input of 60 kJ from the surroundings. The volume after expansion has occurred isothermally is 0.4 m3 . Assuming air behaves as an ideal gas, calculate: (i) thermal efficiency for the cycle (ii) pressure and volume at the beginning of the isothermal expansion, in kPa and m3 , respectively. (iii) the work and heat transfer for each of the four processes, in kJ.

A piston/cylinder system initially holds air at a pressure of 5.5 psig in a volume of 1 ft^3. The ambient pressure oitside the cylinder is 14.5 psia. The cylinder sits in an insulated bath containing 60 lbm of water. The contents are compressed to 100 psia. Intially they both have a temp of 50 F. After compression both air and water have a final temp of 51 F

a) Find the mass of air in cylinder in lbm

b) Hiw much work was supplied in . compression process? in BTU

Five grams of the specified pure solvent is placed in a variable volume piston. What are the molar enthalpy and total enthalpy of the pure system when 50% and 75% have been evaporated at (i) 30C, (ii) 50C. Use liquid at 25C as a reference state. a) Benzene (liquid density = 0.88 g/cm3) b) Ethanol (liquid density = 0.79 g/cm3) c) Water without using the steam tables (liquid density = 1 g/cm3) d) Water using the steam tabless

Carbon monoxide gas (CO) contained within a piston– cylinder assembly undergoes three processes in series:

Process 1–2: Expansion from p₁ = 4.5 bar, V₁ = 0.8 m³ to V₂ = 1.4 m³, during which the pressure-volume relationship is pV = constant.

Process 2–3: Constant-volume heating from state 2 to state 3, where p₃ = 4.5 bar.

Process 3–1: Constant-pressure compression to the initial state.

Evaluate the overall work, in kJ and graph

Q2. Two kilograms of air within a piston-cylinder configuration execute a Carnot power cycle between temperatures 750 K and 300 K. The isothermal expansion is associated with a release of 60 kJ of heat into the surroundings. The volume after expansion has occurred isothermally is 0.4 m3 . Assuming air behaves as an ideal gas, calculate: (i) thermal efficiency for the cycle (ii) pressure and volume at the beginning of the isothermal expansion, in kPa and m3 , respectively. (iii) the work and heat transfer for each of the four processes, in kJ.

A cylinder with a piston contains 0.160 mol of nitrogen at 1.80×105 Pa and 310 K . The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure.

a.) Find the work done by the gas during the adiabatic expansion.

b.) Find the heat added to the gas during the adiabatic expansion.

c.) Find the internal-energy change of the gas during the adiabatic expansion.