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# Probability

### Calculating probabilities: 3 questions.

1) The odds of the Dallas Cowboys winning this year's Super Bowl are 3 to 1. Compute the probability of the Cowboys winning a).33 b).25 c).75 d) none. 2) An appliance dealer calculated the proportion of new dishwashers sold that required various numbers of service calls to correct problems during the warranty period. The r

### Probabilities and conditional probabilities.

I have been struggling with theses two following problems: illustration: age a(0.00%) b(0.01-0.9%) c(>_0.10%) d 0-19 142 7 6 155 e 20-39 47 8 41 96 f 40-59 29 8 77

### Determining an Expected Value of a Random Variable

Suppose you want to sell your house and you have decided to accept the first offer exceeding M dollars, say. Assume that the offers are i.i.d. with common distribution F. Find the expected number of offers received before selling the house. I do not really know how to start the problem. I expect that I have to use either the

### Calculating probability...

All Seasons Plumbing has two service trucks which frequently break down. If the probability the first truck is available is .75, the probability the second truck is available is .50, and the probability that both trucks are available is .30, what is the probability neither truck is available?

### Systems Engineering or Statics for MTBF and probability of failure

Please review these attached Systems Engineering problems and provide assistance. The problems are related to Mean Time Between Failure and failure rates for systems. --------------------------------------------------------------------- 10. The failure rate (&#955;) of a device is 22 failures per million hours. Two standby

### STATISCAL ANALYSIS

Details: Using our data set from Unit 1, compose an email to the head of the American Intellectual Union which discusses the following: Begin your email to AIU by first providing an overview of the database, i.e. a story. Be sure to include information about how you would use the concept of probabilities to apply to prof

### Probability

If A and B are independent events with P(A) = 0.25 and P(B) = 0.60, then P(A/B) is? 2. Intentions of customers regarding future automobile purchases and the financial capability of the consumers are given below: Plan to buy qualify for within 6 6 months or

### Probability ...

1. The salaries (in thousands of dollars) for a sample of 13 employees of a firm are: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8 and 28.2. Compute the variances. 2. New York City is estimated to have 21 percent of the homes with TV sets served by cable TV. If a random sample of four is taken f

### Statistics - Probability..

In a bag there are 20 marbles. The colors of the marbles are as follows: red - 5; blue - 8; green - 3; yellow - 4. a. What is the probability of selecting a red marble? b. What is the probability of selecting a blue marble? c. What is the probability of selecting a pink marble? None d. What is the probability of selectin

### Probability...

New Orleans Punch was made by Frutayuda, Inc., and sold in 16-ounce cans to benefit victims of Hurricane Katrina. The mean number of ounces placed in a can by an automatic fill pump is 15.8 with a standard deviation of 0.12 ounce. Assuming a normal distribution, what is the probability that the filling pump will cause an overflo

### Probability and Z-score Calculations

Tony Soprano and his "weasily" nephew Christopher were scheming on how they can rip off people through their waste management company. One of the ideas they are contemplating is giving everyone a much larger garbage can so they can charge higher rates. After all, the more garbage they pick up the more they can charge. Tony and C

### Probability and z-score

New car manufacturer claims that miles per gallon for gas consumption is mound shaped and symmetric with a mean of 25.9 mpg with a standard deviation of 9.5 mpg. If 30 cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Answer rounded to the nearest 4 decimal places.

### Normal Distribution: Example Problem

Electrical connectors manufactured by a supply company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. The company agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many do the company expect to replace on average? Answer to ne

### Probability

The average hourly wage of workers at a fast food restaurant is \$6.50/hr with a standard deviation of \$0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than \$6.75? Answer rounded to 4 decimal places.

### Statistics - Probability..

Suppose that the probability that a new medication will cause a bad side effect is 0.03. If this medication is given to 150 people, what is the probability that exactly three of them will experience a bad side effect. Answer rounded to 4 decimal places.

### Probability - The length of time to complete a door assembly on ...

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and a standard deviation 2.2 minutes. For a door selected at random, what is the probability the asembly line time will be between 5 and 10 minutes? Answer to 4 decimal places.

### Probability using normal distribution explained in this solution

1. Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 135 tomatoes per day and a standard deviation equal to 30 tomatoes per day. How many tomatoes must be available on any given da

### Distribution Probability: Vacation Destinations

57% of families say that their children have an influence on their vacation destinations. Consider a random sample of six families who are asked if their children have an influence on their vacation destination. (a) Construct a binomial distribution (b) Find the mean, variance and standard deviation of the distribution

### Understanding and calculating probabilities.

1. A certain company reduced its management staff from 18 managers to 12. The company claimed that the 6 managers were randomly selected for job termination. However, the 6 managers chosen are the 6 oldest managers among the 18 that were employed. What is the probability that when 6 oldest managers are randomly selected from

### Defective Blackberries, Ripe Tomatoes

1.Suppose that in an assortment of 20 blackberries, there are 5 with defective switches. In a draw without replacement, if 3 blackberries are picked at random, what is the probability that all 3 have defective switches? 2.A tray of 20 tomatoes has a 12.5% probability of being too ripe. What is the probability that exactly 3

### Linear Programming (LP) Problem. Assuming these numbers to be representative, and that transfers /re-enrollment occur twice yearly, what will be the market share distribution at the end of the next cycle? What will be the market distribution at the end of the next year? What will be the market distribution at the end of the 5-year planning period of interest to the Dean? If changes are not made that effect a change in the enrollment rate, the assumptions for a steady state population (exits=entrants) hold true, and there are no other significant schools entering the competition that changes the numbers for "other" category, what will be the distribution when the competition for students "steady out" (reaches steady state)?

E-1. The market for on-line degrees and courses is becoming crowded and quality and responsiveness seem to play a role in attracting students to continue in a program. The Academic Dean of Ed Marshal Automotive University (EMAU) is interested in how EMAU is doing in the on-line area. He commissioned a study by a faculty-staff

### Probability: Discrete and Continuous Probability Distributions

What is a probability distribution and its purpose? Distinguish between discrete and continuous probability distributions. Give an example of each. What is randomness? Assume you have an Excel worksheet of the dimension, A1:E101. The first row contains data labels. How would you randomize the data file and to select a

### Utilization Rates, Down Times, and Probabilities

19. "Fast Eddie" Flournoy manages the service equipment division of Delta Airline's Atlanta terminal. He keeps a service crew on call to repair tow tractors that break down. Tractors break down on an average of three per day. The repair crew could service an average of 8 tractors per day. "Fast Eddie", a real math whiz, estima

### LP Problem: critical path, completion time, and probabilities.

*18. DEF A/C Remodelers has contracted to reconfigure the interior of a large corporate A/C. The project manager has determined that there are 11 steps to the process. In consultation with the project foreman he has determined the sequence and precedent for the 11 events, labeled A - K, and has estimated the optimistic, expe

### How do you use a decision tree to decide whether to build a small or a large plant at a new location?

A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either small or large, with probabilities estimated to be 0.4 and 0.6 respectively. If a small plant is built, and demand is large, the production manager may choose to maintain the current size or to expand. The

### Calculating joint pmf, conditional pmf, finding covariance

1) suppose that you repeatedly toss a coin whoes probability of head is p. Let X denote the number of tosses needed to get the first head and Y denote the number of tosses needed to get the second toss. a) Find the joint pmf of X and Y. b) Find the conditional pmf of Y given X=x. c) Are X and Y independent? d) (Bonus) Find

### Problems with probabilities

Please help with the following probability problem. A statistical experiment involves flipping a coin that is much thicker than a regular coin of the same diameter. When flipped, the probability for the thick coin to come to rest on its edge is 4 percent; otherwise it is a "fair coin" in the sense that we can get heads or ta

### Simulation of probability distributions

Every 5 minutes a satellite sends an almost instantaneous signal burst to a ground station to communicate that all systems are working properly. The satellite will not transmit the burst if there is an error somewhere. The transmitted signal strength is 4 units. The signal received at the ground station is a combination of the t

### Fault Tree Problem: Calculating probabilities.

Assume the probability of a tire blowout is 0.178% per 50,000 miles of use and that a person travels 15,000 miles per year in a car. Assume that the probability of loss of control is 60% if the blowout occurs on the front tires and 20% for the rear tires. If control is lost, the probability is 50% of veering to the right and 50%

### Conduct a simulation for 20 copier arrivals assuming that the system starts empty. Use the Excel random number function to determine the inspection times. Calculate the average time a copier spends in the system based on these 20 arrivals.

Ricon, Inc. uses an assembly line to produce its office copiers. The final step in the assembly process is quality control inspection. Copiers arrive at the quality inspection area exactly every 90 seconds. The time it takes to perform a quality control inspection follows an exponential distribution, with a mean of 72 seconds