How to answer to the questions based on the case below?

You are the newly appointed Purchasing Director for an international company sourcing material from suppliers in different continents. You found that in recent years, there has been a number of incidents happened that caused significant disruptions to the supply chain. A consultant hired by the company recommend using a probability/impact model to analyse supply chain risks and plan appropriate responses.

1. Explain the risk probability/impact analytical model
2. Provide an example of a high probability / low impact risk and recommend a response
3. Provide an example of a low probability / high impact risk and recommend a response

1. Theater tickets for a hit show have four prices depending on seating. The prices ae $50, $100, $150 and $200. The probability a ticket sells for $50 is .4. The probability it sells for $100 is .15. The probability it sells for $150 is .2.

1. Find the probability a ticket sells for $200.

2. Find the expected cost (mean cost) of a ticket.

3. Find the standard deviation for the cost of a ticket

4. Find the variance for the cost of a ticket

2. A person pays $2.00 to play the following carnival game: A die is rolled one time. If an even number comes up the person pays an additional $2.50. If it comes up odd, the player receives a payment of $5.00 and gets the $2.00 back. Find the players expected profit if (s)he plays this game.

3. Sixty percent of all shoppers in a given shopping center use credit cards for their purchases. If 20 shoppers make purchases, find the probability that:

1. exactly 12 use credit cards.

2. exactly 7 do not use credit cards.

3. At most 10 use credit cards

4. More than 13 use credit cards

4. The probability a person passes the Bar exam is .46. If 290 people in this city take the exam:

1. Find the mean number who pass.

2. Find the standard deviation for the number who pass.

5. Find each of the following probabilities for a value chosen at random from a Standard Normal (Z) distribution.

1. the probability the value is more than 2.7

2. the probability the value is between –2.01 and 2.21

3. The probability the value is less than –3.2

6. The hourly wage for workers in a fast food restaurant is Normally distributed with a mean of $5.85 and a standard deviation of $0.35. If a worker is selected at random, find the probability that:

1. (S)he earns less than $5.50 an hour

2. (S)he earns between $5.90 and $6.40 an hour.

3. (S)he earns at least $6.00 an hour

7. The mean cost of living for a family of four in cities across the country is $65,351 with a standard deviation of $7712. A company is thinking of relocating to a city with a cost of living that is in the bottom 40% of all the cities. Assuming that the distribution is Normally distributed, what is the cutoff score for a city that would make it eligible for consideration by this company?

8. 45% of people have type O blood . If 400 volunteers show up to donate blo, use the Normal approximation to the binomial to find the probability that more than 175 but at most 182 have type O blood.

9. The mean annual rainfall in a particular region is 80 inches with a standard deviation of 8 inches. If a sample of 32 years is selected, what is the probability that the mean annual rainfall for this sample will be less than 79 inches?

let's think about flipping a coin and gettings lots of heads in a row.

What threshold would you use for deciding the coin was not fair? What probability of getting some number of heads in a row would you use to decide the coin was baised?

How many heads in a row would you need to get to reach your probability threshold?

let's think about flipping a coin and gettings lots of heads in a row. What threshold would you use for deciding the coin was not fair? What probability of getting some number of heads in a row would you use to decide the coin was baised? How many heads in a row would you need to get to reach your probability threshold?

(a) Find the probability of being dealt a "nines over kings" full house (three nines and two kings). (Round your answer to six decimal places.)

(b) Find the number of different types of full houses. (Ignoring suit.)
ways

(c) Find the probability of being dealt a full house. (Round your answer to six decimal places.)

Assume that a gender selection method was used by a couple trying to conceive a girl. Let x be the number of girls in three births. Assuming that the probability of using this gender selection method is 63% effective in conceiving a girl, list the probability distribution of a couple having three children.

(Please show all work.)

A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defective items in the sample. To look up the probability of a defective item being drawn from the box, using a binomial probability table, what would be the values of n, x and p to look up?

Consider an Erlang service system (M / Ek / 1) in which no queue is allowed to form. Let n = the number of stages of service left in the system, and let pn be the equilibrium probability of being in state n.

(a) Write flow balance equations.

(b) Find an expression for pn, n = 0, 1, ..., k

(c) Find the probability of a busy system.

Suppose that, in a given population, the probability of success for a given drug is 0.7 for men and 0.5 for women (the researchers cannot be aware of this). In a study to determine the probability of success, 7 men and 14 women were assigned to receive the drug (no blocking was performed; all were lumped in to the treatment group). What is the bias in this study for each biological sex? (This may be a positive or a negative number).